Verificación de la evolución de la mortalidad a través de los años

[ES] Típicos enfoques de análisis y graduación de la mortalidad se basan en la no dinamicidad, y por tanto estabilidad de ésta, para periodos largos de tiempo. Por el contrario, este artículo está enfocado sobre un factor relevante en la evolución de la misma, como es el tiempo cronológico. Así pues, el objetivo de este trabajo es analizar la influencia que tiene el tiempo cronológico en las probabilidades anuales de muerte de un individuo de edad x, qx, cuando las probabilidades están tanto graduadas (suavizadas) como sin graduar (sin suavizar). Para ello, se calculan las estimaciones de dichas probabilidades con datos del INE de la Comunidad Valenciana, referidos estos a diferentes periodos de tiempo. Los resultados del estudio empírico parecen confirmar la existencia de diferencias entre las experiencias de mortalidad y comportamientos correspondientes a periodos de tiempo cronológico distintos tanto para hombres como para mujeres. Estas conclusiones ratifican una vez más, la utilidad de las tablas de mortalidad dinámicas en el ámbito de las operaciones actuarialesDebón Aucejo, AM. (2004). Verificación de la evolución de la mortalidad a través de los años. Rect@ Revista Electrónica de Comunicaciones y Trabajos de ASEPUMA. 5(1):65-82. http://hdl.handle.net/10251/134995S65825

Do corporate websites' changes reflect firms' survival?

This article is (c) Emerald Group Publishing and permission has been granted for this version to appear here http://doi.org/10.1108/OIR-11-2016-0321. Emerald does not grant permission for this article to be further copied/distributed or hosted elsewhere without the express permission from Emerald Group Publishing Limited[EN] Purpose The purpose of this paper is to analyze to what extent changes in corporate websites reflect firms' survival. Since keeping a website online involves some costs, it is likely that firms would invest resources on it only when they are active and healthy. Therefore, when a firm dies, this event is likely to be manifested on its website as lacking updates or being down. Design/methodology/approach Changes in the corporate websites of a panel of Spanish firms were tracked between 2008 and 2014 in order to evaluate the approach. The status of websites, classified according to the type of change undergone, was used to infer firms' activity status (active or inactive). Multi-period logistic regressions and a duration model were applied to study the relationship among the website status and the firm's status. Findings Results showed that changes in website contents clearly reflect the firm's status. Active firms were mainly associated with updated corporate websites, while inactive firms were more associated with down websites. In fact, results confirmed that the firms' death hazard increases when the website activity lowers. Originality/value Although online information is increasingly being used to monitor the economy, this is the first study to connect online data to firms' survival. The results revealed a new source of information about business demography and evidenced corporate websites as a fresh source of high granularity business data.This work has been partially supported by the Spanish Ministry of Economy and Competitiveness with Grants TIN2013-43913-R and MTM2013-45381-P-AR, and by the Spanish Ministry of Education with Grant FPU14/02386. The authors thank the participants of the "1st International Conference on Advanced Research Methods and Analytics (CARMA2016)" for their invaluable comments.Blazquez, D.; Domenech, J.; Debón Aucejo, AM. (2018). Do corporate websites' changes reflect firms' survival?. Online Information Review. 42(6):956-970. https://doi.org/10.1108/OIR-11-2016-0321S95697042

A Comparison of Forecasting Mortality Models Using Resampling Methods

[EN] The accuracy of the predictions of age-specific probabilities of death is an essential objective for the insurance industry since it dramatically affects the proper valuation of their products. Currently, it is crucial to be able to accurately calculate the age-specific probabilities of death over time since insurance companies' profits and the social security of citizens depend on human survival; therefore, forecasting dynamic life tables could have significant economic and social implications. Quantitative tools such as resampling methods are required to assess the current and future states of mortality behavior. The insurance companies that manage these life tables are attempting to establish models for evaluating the risk of insurance products to develop a proactive approach instead of using traditional reactive schemes. The main objective of this paper is to compare three mortality models to predict dynamic life tables. By using the real data of European countries from the Human Mortality Database, this study has identified the best model in terms of the prediction ability for each sex and each European country. A comparison that uses cobweb graphs leads us to the conclusion that the best model is, in general, the Lee-Carter model. Additionally, we propose a procedure that can be applied to a life table database that allows us to choose the most appropriate model for any geographical area.The research of David Atance was supported by a grant (Contrato Predoctoral de Formacion Universitario) from the University of Alcala. This work is partially supported by a grant from the MEIyC (Ministerio de Economia, Industria y Competitividad, Spain project ECO2017-89715-P).Atance, D.; Debón Aucejo, AM.; Navarro, E. (2020). A Comparison of Forecasting Mortality Models Using Resampling Methods. Mathematics. 8(9):1-21. https://doi.org/10.3390/math8091550S12189BOOTH, H., MAINDONALD, J., & SMITH, L. (2002). Applying Lee-Carter under conditions of variable mortality decline. Population Studies, 56(3), 325-336. doi:10.1080/00324720215935Brouhns, N., Denuit, M., & Vermunt, J. K. (2002). A Poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics, 31(3), 373-393. doi:10.1016/s0167-6687(02)00185-3Lee, R., & Miller, T. (2001). Evaluating the performance of the lee-carter method for forecasting mortality. Demography, 38(4), 537-549. doi:10.1353/dem.2001.0036Cairns, A. J. G., Blake, D., & Dowd, K. (2006). A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration. Journal of Risk & Insurance, 73(4), 687-718. doi:10.1111/j.1539-6975.2006.00195.xCairns, A. J. G., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., Ong, A., & Balevich, I. (2009). A Quantitative Comparison of Stochastic Mortality Models Using Data From England and Wales and the United States. North American Actuarial Journal, 13(1), 1-35. doi:10.1080/10920277.2009.10597538Renshaw, A. E., & Haberman, S. (2003). Lee–Carter mortality forecasting with age-specific enhancement. Insurance: Mathematics and Economics, 33(2), 255-272. doi:10.1016/s0167-6687(03)00138-0Renshaw, A. E., & Haberman, S. (2006). A cohort-based extension to the Lee–Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38(3), 556-570. doi:10.1016/j.insmatheco.2005.12.001Hainaut, D. (2018). A NEURAL-NETWORK ANALYZER FOR MORTALITY FORECAST. ASTIN Bulletin, 48(02), 481-508. doi:10.1017/asb.2017.45Levantesi, S., & Pizzorusso, V. (2019). Application of Machine Learning to Mortality Modeling and Forecasting. Risks, 7(1), 26. doi:10.3390/risks7010026Pascariu, M. D., Lenart, A., & Canudas-Romo, V. (2019). The maximum entropy mortality model: forecasting mortality using statistical moments. Scandinavian Actuarial Journal, 2019(8), 661-685. doi:10.1080/03461238.2019.1596974S̀liwka, P., & Socha, L. (2018). A proposition of generalized stochastic Milevsky–Promislov mortality models. Scandinavian Actuarial Journal, 2018(8), 706-726. doi:10.1080/03461238.2018.1431805Lyons, M. B., Keith, D. A., Phinn, S. R., Mason, T. J., & Elith, J. (2018). A comparison of resampling methods for remote sensing classification and accuracy assessment. Remote Sensing of Environment, 208, 145-153. doi:10.1016/j.rse.2018.02.026Molinaro, A. M., Simon, R., & Pfeiffer, R. M. (2005). Prediction error estimation: a comparison of resampling methods. Bioinformatics, 21(15), 3301-3307. doi:10.1093/bioinformatics/bti499Arlot, S., & Celisse, A. (2010). A survey of cross-validation procedures for model selection. Statistics Surveys, 4(none). doi:10.1214/09-ss054Stone, M. (1974). Cross-Validatory Choice and Assessment of Statistical Predictions. Journal of the Royal Statistical Society: Series B (Methodological), 36(2), 111-133. doi:10.1111/j.2517-6161.1974.tb00994.xBergmeir, C., Hyndman, R. J., & Koo, B. (2018). A note on the validity of cross-validation for evaluating autoregressive time series prediction. Computational Statistics & Data Analysis, 120, 70-83. doi:10.1016/j.csda.2017.11.003Efron, B. (1979). Bootstrap Methods: Another Look at the Jackknife. The Annals of Statistics, 7(1). doi:10.1214/aos/1176344552Brouhns, N., Denuit *, M., & Van Keilegom, I. (2005). Bootstrapping the Poisson log-bilinear model for mortality forecasting. Scandinavian Actuarial Journal, 2005(3), 212-224. doi:10.1080/03461230510009754D’Amato, V., Haberman, S., Piscopo, G., & Russolillo, M. (2012). Modelling dependent data for longevity projections. Insurance: Mathematics and Economics, 51(3), 694-701. doi:10.1016/j.insmatheco.2012.09.008Debón, A., Martínez-Ruiz, F., & Montes, F. (2012). Temporal Evolution of Mortality Indicators. North American Actuarial Journal, 16(3), 364-377. doi:10.1080/10920277.2012.10590647Debón, A., Montes, F., Mateu, J., Porcu, E., & Bevilacqua, M. (2008). Modelling residuals dependence in dynamic life tables: A geostatistical approach. Computational Statistics & Data Analysis, 52(6), 3128-3147. doi:10.1016/j.csda.2007.08.006Koissi, M.-C., Shapiro, A. F., & Högnäs, G. (2006). Evaluating and extending the Lee–Carter model for mortality forecasting: Bootstrap confidence interval. Insurance: Mathematics and Economics, 38(1), 1-20. doi:10.1016/j.insmatheco.2005.06.008Liu, X., & Braun, W. J. (2010). Investigating Mortality Uncertainty Using the Block Bootstrap. Journal of Probability and Statistics, 2010, 1-15. doi:10.1155/2010/813583Härdle, W., Horowitz, J., & Kreiss, J. (2003). Bootstrap Methods for Time Series. International Statistical Review, 71(2), 435-459. doi:10.1111/j.1751-5823.2003.tb00485.xBergmeir, C., & Benítez, J. M. (2012). On the use of cross-validation for time series predictor evaluation. Information Sciences, 191, 192-213. doi:10.1016/j.ins.2011.12.028Booth, H., Hyndman, R. J., Tickle, L., & de Jong, P. (2006). Lee-Carter mortality forecasting: a multi-country comparison of variants and extensions. Demographic Research, 15, 289-310. doi:10.4054/demres.2006.15.9Delwarde, A., Denuit, M., & Eilers, P. (2007). Smoothing the Lee–Carter and Poisson log-bilinear models for mortality forecasting. Statistical Modelling, 7(1), 29-48. doi:10.1177/1471082x0600700103Debón, A., Montes, F., & Puig, F. (2008). Modelling and forecasting mortality in Spain. European Journal of Operational Research, 189(3), 624-637. doi:10.1016/j.ejor.2006.07.050Currie, I. D., Durban, M., & Eilers, P. H. (2004). Smoothing and forecasting mortality rates. Statistical Modelling, 4(4), 279-298. doi:10.1191/1471082x04st080oaChen, K., Liao, J., Shang, X., & Li, J. S.-H. (2009). «A Quantitative Comparison of Stochastic Mortality Models Using Data from England and Wales and the United States,» Andrew J. G. Cairns, David Blake, Kevin Dowd, Guy D. Coughlan, David Epstein, Alen Ong, and Igor Balevich, Vol. 13, No. 1, 2009. North American Actuarial Journal, 13(4), 514-520. doi:10.1080/10920277.2009.10597572Plat, R. (2009). On stochastic mortality modeling. Insurance: Mathematics and Economics, 45(3), 393-404. doi:10.1016/j.insmatheco.2009.08.006Debón, A., Martínez-Ruiz, F., & Montes, F. (2010). A geostatistical approach for dynamic life tables: The effect of mortality on remaining lifetime and annuities. Insurance: Mathematics and Economics, 47(3), 327-336. doi:10.1016/j.insmatheco.2010.07.007Yang, S. S., Yue, J. C., & Huang, H.-C. (2010). Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models. Insurance: Mathematics and Economics, 46(1), 254-270. doi:10.1016/j.insmatheco.2009.09.013Haberman, S., & Renshaw, A. (2011). A comparative study of parametric mortality projection models. Insurance: Mathematics and Economics, 48(1), 35-55. doi:10.1016/j.insmatheco.2010.09.003Mitchell, D., Brockett, P., Mendoza-Arriaga, R., & Muthuraman, K. (2013). Modeling and forecasting mortality rates. Insurance: Mathematics and Economics, 52(2), 275-285. doi:10.1016/j.insmatheco.2013.01.002Danesi, I. L., Haberman, S., & Millossovich, P. (2015). Forecasting mortality in subpopulations using Lee–Carter type models: A comparison. Insurance: Mathematics and Economics, 62, 151-161. doi:10.1016/j.insmatheco.2015.03.010Yang, B., Li, J., & Balasooriya, U. (2014). Cohort extensions of the Poisson common factor model for modelling both genders jointly. Scandinavian Actuarial Journal, 2016(2), 93-112. doi:10.1080/03461238.2014.908411Neves, C., Fernandes, C., & Hoeltgebaum, H. (2017). Five different distributions for the Lee–Carter model of mortality forecasting: A comparison using GAS models. Insurance: Mathematics and Economics, 75, 48-57. doi:10.1016/j.insmatheco.2017.04.004University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany)www.mortality.orgHunt, A., & Blake, D. P. (2015). Identifiability in Age/Period/Cohort Mortality Models. SSRN Electronic Journal. doi:10.2139/ssrn.3552213Generalized Nonlinear Models in R: An Overview of the Gnm Packagehttps://cran.r-project.org/package=gnmLachenbruch, P. A., & Mickey, M. R. (1968). Estimation of Error Rates in Discriminant Analysis. Technometrics, 10(1), 1-11. doi:10.1080/00401706.1968.10490530Tashman, L. J. (2000). Out-of-sample tests of forecasting accuracy: an analysis and review. International Journal of Forecasting, 16(4), 437-450. doi:10.1016/s0169-2070(00)00065-0Diaz, G., Debón, A., & Giner-Bosch, V. (2018). Mortality forecasting in Colombia from abridged life tables by sex. Genus, 74(1). doi:10.1186/s41118-018-0038-6Ahcan, A., Medved, D., Olivieri, A., & Pitacco, E. (2014). Forecasting mortality for small populations by mixing mortality data. Insurance: Mathematics and Economics, 54, 12-27. doi:10.1016/j.insmatheco.2013.10.013FORSYTHE, A., & HARTICAN, J. A. (1970). Efficiency of confidence intervals generated by repeated subsample calculations. Biometrika, 57(3), 629-639. doi:10.1093/biomet/57.3.629BURMAN, P. (1989). A comparative study of ordinary cross-validation, v-fold cross-validation and the repeated learning-testing methods. Biometrika, 76(3), 503-514. doi:10.1093/biomet/76.3.503Shao, J. (1993). Linear Model Selection by Cross-validation. Journal of the American Statistical Association, 88(422), 486-494. doi:10.1080/01621459.1993.10476299Li, H., & O’Hare, C. (2019). Mortality Forecasting: How Far Back Should We Look in Time? Risks, 7(1), 22. doi:10.3390/risks7010022Breiman, L., & Spector, P. (1992). Submodel Selection and Evaluation in Regression. The X-Random Case. International Statistical Review / Revue Internationale de Statistique, 60(3), 291. doi:10.2307/1403680Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716-723. doi:10.1109/tac.1974.1100705Schwarz, G. (1978). Estimating the Dimension of a Model. The Annals of Statistics, 6(2). doi:10.1214/aos/1176344136Hunt, A., & Blake, D. (2014). A General Procedure for Constructing Mortality Models. North American Actuarial Journal, 18(1), 116-138. doi:10.1080/10920277.2013.852963Moritz, S., & Bartz-Beielstein, T. (2017). imputeTS: Time Series Missing Value Imputation in R. The R Journal, 9(1), 207. doi:10.32614/rj-2017-009Holt-Lunstad, J., Smith, T. B., & Layton, J. B. (2010). Social Relationships and Mortality Risk: A Meta-analytic Review. PLoS Medicine, 7(7), e1000316. doi:10.1371/journal.pmed.100031

Multivariate Control Chart and Lee-Carter Models to Study Mortality Changes

[EN] The mortality structure of a population usually reflects the economic and social development of the country. The purpose of this study was to identify moments in time and age intervals at which the observed probability of death is substantially different from the pattern of mortality for a studied period. Therefore, a mortality model was fitted to decompose the historical pattern of mortality. The model residuals were monitored by the T-2 multivariate control chart to detect substantial changes in mortality that were not identified by the model. The abridged life tables for Colombia in the period 1973-2005 were used as a case study. The Lee-Carter model collects information regarding violence in Colombia. Therefore, the years identified as out-of-control in the charts are associated with very early or quite advanced ages of death and are inversely related to the violence that did not claim as many victims at those ages. The mortality changes identified in the control charts pertain to changes in the population's health conditions or new causes of death such as COVID-19 in the coming years. The proposed methodology is generalizable to other countries, especially developing countries.This research received external funding from the Universitat Politecnica de Valencia (UPV) and the Universidad del Tolima (UT) to cover translation and publication costs.Diaz-Rojo, G.; Debón Aucejo, AM.; Mosquera, J. (2020). Multivariate Control Chart and Lee-Carter Models to Study Mortality Changes. Mathematics. 8(11):1-17. https://doi.org/10.3390/math8112093S117811Alexopoulos, A., Dellaportas, P., & Forster, J. J. (2018). Bayesian forecasting of mortality rates by using latent Gaussian models. Journal of the Royal Statistical Society: Series A (Statistics in Society), 182(2), 689-711. doi:10.1111/rssa.12422Callot, L., Haldrup, N., & Kallestrup-Lamb, M. (2015). Deterministic and stochastic trends in the Lee–Carter mortality model. Applied Economics Letters, 23(7), 486-493. doi:10.1080/13504851.2015.1083075Carfora, M. F., Cutillo, L., & Orlando, A. (2017). A quantitative comparison of stochastic mortality models on Italian population data. Computational Statistics & Data Analysis, 112, 198-214. doi:10.1016/j.csda.2017.03.012Booth, H., Hyndman, R. J., Tickle, L., & de Jong, P. (2006). Lee-Carter mortality forecasting: a multi-country comparison of variants and extensions. Demographic Research, 15, 289-310. doi:10.4054/demres.2006.15.9Salhi, Y., & Loisel, S. (2016). Basis risk modelling: a cointegration-based approach. Statistics, 51(1), 205-221. doi:10.1080/02331888.2016.1259806Postigo-Boix, M., Agüero, R., & Melús-Moreno, J. L. (2019). An alternative procedure to obtain the mortality rate with non-linear functions: Application to the case of the Spanish population. PLOS ONE, 14(10), e0223789. doi:10.1371/journal.pone.0223789Belliard, M., & Williams, I. (2013). Proyección estocástica de la mortalidad. Una aplicación de Lee-Carter en la Argentina. Revista Latinoamericana de Población, 7(13), 129-148. doi:10.31406/relap2013.v7.i2.n13.6García Guerrero, V. M., & Ordorica Mellado, M. (2012). Proyección estocástica de la mortalidad mexicana por medio del método de Lee-Carter / Stochastic Projection of Mexican Mortality through the Lee-Carter Method. Estudios Demográficos y Urbanos, 27(2), 409. doi:10.24201/edu.v27i2.1418Diaz, G., Debón, A., & Giner-Bosch, V. (2018). Mortality forecasting in Colombia from abridged life tables by sex. Genus, 74(1). doi:10.1186/s41118-018-0038-6Mason, R. L., Tracy, N. D., & Young, J. C. (1995). Decomposition ofT2 for Multivariate Control Chart Interpretation. Journal of Quality Technology, 27(2), 99-108. doi:10.1080/00224065.1995.11979573Shewhart, W. A. (1927). Quality Control. Bell System Technical Journal, 6(4), 722-735. doi:10.1002/j.1538-7305.1927.tb00215.xWoodall, W. H. (2006). The Use of Control Charts in Health-Care and Public-Health Surveillance. Journal of Quality Technology, 38(2), 89-104. doi:10.1080/00224065.2006.11918593Vetter, T. R., & Morrice, D. (2019). Statistical Process Control. Anesthesia & Analgesia, 128(2), 374-382. doi:10.1213/ane.0000000000003977Benneyan, J. C. (2003). Statistical process control as a tool for research and healthcare improvement. Quality and Safety in Health Care, 12(6), 458-464. doi:10.1136/qhc.12.6.458Imam, N., Spelman, T., Johnson, S. A., & Worth, L. J. (2019). Statistical Process Control Charts for Monitoring Staphylococcus aureus Bloodstream Infections in Australian Health Care Facilities. Quality Management in Health Care, 28(1), 39-44. doi:10.1097/qmh.0000000000000201Williamson, G. D., & Weatherby Hudson, G. (1999). A monitoring system for detecting aberrations in public health surveillance reports. Statistics in Medicine, 18(23), 3283-3298. doi:10.1002/(sici)1097-0258(19991215)18:233.0.co;2-zThacker, S. B., Stroup, D. F., Rothenberg, R. B., & Brownson, R. C. (1995). Public health surveillance for chronic conditions: A scientific basis for decisions. Statistics in Medicine, 14(5-7), 629-641. doi:10.1002/sim.4780140520Yue, J., Lai, X., Liu, L., & Lai, P. B. S. (2017). A new VLAD-based control chart for detecting surgical outcomes. Statistics in Medicine, 36(28), 4540-4547. doi:10.1002/sim.7362Chamberlin, W. H., Lane, K. A., Kennedy, J. N., Bradley, S. D., & Rice, C. L. (1993). Monitoring intensive care unit performance using statistical quality control charts. International Journal of Clinical Monitoring and Computing, 10(3), 155-161. doi:10.1007/bf01246449Marshall, T., & Mohammed, M. A. (2007). Case-mix and the use of control charts in monitoring mortality rates after coronary artery bypass. BMC Health Services Research, 7(1). doi:10.1186/1472-6963-7-63Briceno-Leon, R., Villaveces, A., & Concha-Eastman, A. (2008). Understanding the uneven distribution of the incidence of homicide in Latin America. International Journal of Epidemiology, 37(4), 751-757. doi:10.1093/ije/dyn153Gaviria, A. (2000). Increasing returns and the evolution of violent crime: the case of Colombia. Journal of Development Economics, 61(1), 1-25. doi:10.1016/s0304-3878(99)00059-0Latin American Human Mortality Databasewww.lamortalidad.orgBOOTH, H., MAINDONALD, J., & SMITH, L. (2002). Applying Lee-Carter under conditions of variable mortality decline. Population Studies, 56(3), 325-336. doi:10.1080/00324720215935Renshaw, A. E., & Haberman, S. (2003). Lee–Carter mortality forecasting with age-specific enhancement. Insurance: Mathematics and Economics, 33(2), 255-272. doi:10.1016/s0167-6687(03)00138-0Debón, A., Montes, F., & Puig, F. (2008). Modelling and forecasting mortality in Spain. European Journal of Operational Research, 189(3), 624-637. doi:10.1016/j.ejor.2006.07.050Debón, A., Martínez-Ruiz, F., & Montes, F. (2010). A geostatistical approach for dynamic life tables: The effect of mortality on remaining lifetime and annuities. Insurance: Mathematics and Economics, 47(3), 327-336. doi:10.1016/j.insmatheco.2010.07.007Wang, D., & Lu, P. (2005). Modelling and forecasting mortality distributions in England and Wales using the Lee–Carter model. Journal of Applied Statistics, 32(9), 873-885. doi:10.1080/02664760500163441Renshaw, A. E., & Haberman, S. (2008). On simulation-based approaches to risk measurement in mortality with specific reference to Poisson Lee–Carter modelling. Insurance: Mathematics and Economics, 42(2), 797-816. doi:10.1016/j.insmatheco.2007.08.009Coelho, E., & Nunes, L. C. (2011). Forecasting mortality in the event of a structural change. Journal of the Royal Statistical Society: Series A (Statistics in Society), 174(3), 713-736. doi:10.1111/j.1467-985x.2010.00687.xVillegas, A. M., Kaishev, V. K., & Millossovich, P. (2018). StMoMo: An R Package for Stochastic Mortality Modeling. Journal of Statistical Software, 84(3). doi:10.18637/jss.v084.i03Tracy, N. D., Young, J. C., & Mason, R. L. (1992). Multivariate Control Charts for Individual Observations. Journal of Quality Technology, 24(2), 88-95. doi:10.1080/00224065.1992.12015232Champ, C. W., & Jones-Farmer, L. A. (2007). Properties of Multivariate Control Charts with Estimated Parameters. Sequential Analysis, 26(2), 153-169. doi:10.1080/07474940701247040gnm: Generalized Nonlinear Models. R Package Version 1.0-8https://CRAN.R-project.org/package=gnmqcc: Quality Control Charting. R Package Version 2.7https://CRAN.R-project.org/package=qccUrdinola, B. P., Torres Áviles†, F., & Velasco, J. A. (2017). The Homicide Atlas in Colombia: Contagion and Under-Registration for Small Areas. Cuadernos de Geografía: Revista Colombiana de Geografía, 26(1), 101-118. doi:10.15446/rcdg.v26n1.5542

A geostatistical approach for dynamic life tables: The effect of mortality on remaining lifetime and annuities

Dynamic life tables arise as an alternative to the standard (static) life table, with the aim of incorporating the evolution of mortality over time. The parametric model introduced by Lee and Carter in 1992 for projected mortality rates in the US is one of the most outstanding and has been used a great deal since then. Different versions of the model have been developed but all of them, together with other parametric models, consider the observed mortality rates as independent observations. This is a difficult hypothesis to justify when looking at the graph of the residuals obtained with any of these methods. Methods of adjustment and prediction based on geostatistical techniques which exploit the dependence structure existing among the residuals are an alternative to classical methods. Dynamic life tables can be considered as two-way tables on a grid equally spaced in either the vertical (age) or horizontal (year) direction, and the data can be decomposed into a deterministic large-scale variation (trend) plus a stochastic small-scale variation (residuals). Our contribution consists of applying geostatistical techniques for estimating the dependence structure of the mortality data and for prediction purposes, also including the influence of the year of birth (cohort). We compare the performance of this new approach with different versions of the Lee–Carter model. Additionally, we obtain bootstrap confidence intervals for predicted qxt resulting from applying both methodologies, and we study their influence on the predictions of e65t and a65t . © 2010 Elsevier B.V. All rights reserved.This work was partially supported by grants from the MEyC (Ministerio de Educacin y Ciencia, Spain project MTM2007-62923 and project MTM2008-05152) The research by Ana Debon and Francisco Martinez-Ruiz has also been partially supported by a grant from the Generalitat Valenciana (grant No GVPRE/2008/103)Debón Aucejo, AM.; Martinez Ruiz, F.; Montes, F. (2010). A geostatistical approach for dynamic life tables: The effect of mortality on remaining lifetime and annuities. Insurance: Mathematics and Economics. 47(3):327-336. https://doi.org/10.1016/j.insmatheco.2010.07.007S32733647

Temporal evolution of some mortality indicators: Application to Spanish data

This is an author's accepted manuscript of an article published in: “North American Actuarial Journal"; Volume 16, Issue 3, 2012; copyright Taylor & Francis; available online at: http://dx.doi.org/10.1080/10920277.2012.10590647[EN] In Spain, as in other developed countries, significant changes in mortality patterns have occurred during the 20th and 21st centuries. One reflection of these changes is life expectancy, which has improved in this period, although the robustness of this indicator prevents these changes from being of the same order as those for the probability of death. If, moreover, we bear in mind that life expectancy offers no information as to whether this improvement is the same for different age groups, it is important and necessary to turn to other mortality indicators whose past and future evolution in Spain we are going to study. These indicators are applied to Spanish mortality data for the period 1981–2008, for the age range 0–99. To study its future evolution, the mortality ratios have to be projected using an adequate methodology, namely, the Lee-Carter model. Con- fidence intervals for these predictions can be calculated using the methodology that Lee and Carter apply in their original article for expected lifetime confidence intervals, but they take into account only the error in the prediction of the mortality index obtained from the ARIMA model adjusted to its temporal series, excluding other sources of error such as that introduced by estimations of the other parameters in the model. That is why bootstrap procedures are preferred, permitting the combination of all sources of uncertainty.Support for the research presented in this paper was provided by a grants from MeyC (Ministerio de Educacio´n y Ciencia, Spain), projects MTM2010-14961 and MTM2008-05152. This article was finished in two research stays at Cass Business School (London) funded by ‘‘Jose´ Castillejo’’ Program, Universitat Polite`cnica de Vale`ncia (PAID-00-12) and the Faculty de Administracio´n y Direccio´n de Empresas. We appreciate this funding and the opportunity to discuss our ideas with faculty and doctoral students Cass Business School.Debón Aucejo, AM.; Martínez Ruiz, F.; Montes, F. (2012). Temporal evolution of some mortality indicators: Application to Spanish data. North American Actuarial Journal. 16(3):364-377. https://doi.org/10.1080/10920277.2012.10590647S36437716

Mètodes estadístics per a les assegurances de vida

[CA] L'estudi i evolució de la mortalitat, per les repercussions econòmiques i socials que presenta, és un tema d'elevat interès tant per als actuaris i els estadístics com per als demògrafs. En aquest treball revisem les diferents alternatives per a graduar les probabilitats de mort mitjançant models dinàmics, aquells que prenen en compte simultàniament la influència de l'edat i el temps del calendari, i en mostrem l'aplicació a dades de mortalitat d'Espanya. Finalment, es comenten les tendències futures en l'anàlisi dinàmica de la mortalitat.Aquest treball està parcialment subvencionat per un projecte del MEC (Ministeri d Educació i Ciència, Espanya, projecte MTM-2004-06231). Gràcies també a l Àrea de Promoció i Normalització Lingüística de la Universitat Politècnica de València pel finançament que ha aportat per a aquest treball.Debón Aucejo, AM.; Montes-Suay, F. (2007). Mètodes estadístics per a les assegurances de vida. Butlletí de la Societat Catalana de Matemàtiques. 22(1):45-73. http://hdl.handle.net/10251/150646S457322

Estudio de la mortalidad en Colombia, ajuste del modelo de Lee-Carter para su análisis y predicción

[ES] En la actualidad resulta de gran importancia el análisis de los fenómenos como el crecimiento poblacional y la reducción de la mortalidad por la repercusión económica y social que dichos procesos tienen en el desarrollo de los países. En este sentido las tablas de mortalidad constituyen una herramienta para comprender, a través de las probabilidades de muerte, la esperanza de vida y otros indicadores, la dinámica poblacional. Lee y Carter (1992), plantearon un modelo, cuyo ajuste permite a los analistas obtener una visión dinámica del comportamiento de la mortalidad durante un periodo de análisis. En este trabajo se hace uso de este modelo para estudiar la mortalidad en Colombia, utilizando tablas de mortalidad construidas a partir de información suministrada por la base de datos internacional Latin American Human Mortality Database. En los resultados se presentan las comparaciones entre los modelos obtenidos en el periodo 1973-2005. Se observa una reducción de la mortalidad en el periodo analizado y se logra identificar la estructura de la mortalidad para hombres y mujeres, así como una tendencia en la reducción de sus diferencias.[EN] At present, is of great interest the analysis of phenomena such as population growth and reduced mortality by economic and social impact these processes have on developing countries. In this sense, the life tables are a tool for understanding, through the probability of death, life expectancy and other indicators, the population dynamics. Lee and Carter (1992), made a proposal for modeling, whose setting enables to the analysts obtain a dynamic view of the behavior of mortality during a period of analysis. In this work this model is used to study the mortality in Colombia, taking mortality tables, which are constructed from information provided by the international database Latin American Human Mortality Database. The results, show the comparisons among the models obtained in the period 1973-2005. It is observed a reduction in the mortality rate, identifying the structure of mortality for men and women, as well as a tendency to reduce the differences between them.Diaz Rojo, G.; Debón Aucejo, AM. (2016). Estudio de la mortalidad en Colombia, ajuste del modelo de Lee-Carter para su análisis y predicción. Anales de ASEPUMA. 24. http://hdl.handle.net/10251/93246S2

Aproximación intuitiva a algunos tipos de convergencia estocástica

[ES] En este trabajo estudiamos cuatro modos clásicos de convergencia estocástica: en probabilidad, casi segura , en media cuadrática y en distribución. El artículo está basado en la interpretación gráfica a través del software estadístico SPLUS.Cortés, J.; Debón Aucejo, AM. (2002). Aproximación intuitiva a algunos tipos de convergencia estocástica. Epsilon. (54):441-455. http://hdl.handle.net/10251/136037S4414555

A comparison of parametric models for mortality graduation. Application to mortality data of the Valencia Region

[EN] The parametric graduation of mortality data has as its objective the satisfactory estimation of the death rates based on mortality data but using an age-dependent function whose parameters are adjusted from the crude rates obtainable directly from the data. This paper proposes a revision of the most commonly used parametric methods and compares the results obtained with each of them when they are applied to the mortality data for the Valencia Region. As a result of the comparison, we conclude that the Gompertz-Makeham functions estimated by means of generalized linear models lead to the best results. Our working method is of additional interest for being applicable to mortality data for a wide range of ages from any geographical conditions, allowing us to select the most appropriate life table for the case in hand.Debón Aucejo, AM.; Montes-Suay, F.; Sala-Garrido, R. (2005). A comparison of parametric models for mortality graduation. Application to mortality data of the Valencia Region. SORT. Statistics and Operations Research Transactions. 29(2):269-288. http://hdl.handle.net/10251/147780S26928829