An Improved Confidence Interval for The Difference between Standard Deviations of Normal Distributions Using a Ranked Set Sampling

In this paper, a confidence interval is derived for the difference between the standard deviations of normal distributions using the method of variance of estimates recovery. This confidence interval was improved using the estimators of the standard deviations using ranked set sampling (RSS) instead of the standard method using simple random sampling (SRS). An evaluation of the performance of the proposed confidence interval based on RSS compared to the existing one based on SRS was conducted via a Monte Carlo simulation study. The results revealed that the proposed confidence interval based on RSS performed more efficient than the existing one based on SRS in terms of the coverage probability and average length. A confidence interval comparison is also illustrated using a real data example in the area of medical science

Tendencias en la predicción y estimación de los intervalos de confianza usando modelos de redes neuronales aplicados a series temporales

En este artículo, se discute el estado del arte en la estimación de la predicción varios pasos adelante para modelos de series temporales no lineales basados en perceptrones multicapa. Se revisan las principales tendencias para la estimación de pronósticos puntuales e intervalos de confianza. En adición, se argumenta sobre los principales problemas abiertos para investigación futura en la predicción de series temporales usando redes neuronales

Robustness-Based Design Optimization Under Data Uncertainty

This paper proposes formulations and algorithms for design optimization under both aleatory (i.e., natural or physical variability) and epistemic uncertainty (i.e., imprecise probabilistic information), from the perspective of system robustness. The proposed formulations deal with epistemic uncertainty arising from both sparse and interval data without any assumption about the probability distributions of the random variables. A decoupled approach is proposed in this paper to un-nest the robustness-based design from the analysis of non-design epistemic variables to achieve computational efficiency. The proposed methods are illustrated for the upper stage design problem of a two-stage-to-orbit (TSTO) vehicle, where the information on the random design inputs are only available as sparse point and/or interval data. As collecting more data reduces uncertainty but increases cost, the effect of sample size on the optimality and robustness of the solution is also studied. A method is developed to determine the optimal sample size for sparse point data that leads to the solutions of the design problem that are least sensitive to variations in the input random variables

Stochastic Monte Carlo simulations of the pantograph-catenary dynamic interaction to allow for uncertainties introduced during catenary installation

"This is an Accepted Manuscript of an article published by Taylor & Francis inVehicle System Dynamics on APR 3 2019, available online: https://www.tandfonline.com/doi/full/10.1080/00423114.2018.1473617."[EN] The simulation of the pantograph-catenary dynamic interaction is at present mainly based on deterministic approaches. However, any errors made during the catenary stringing process are sources of variability that can affect the dynamic performance of the system. In this paper, we analyse the influence of dropper length, dropper spacing and support height errors on the current collection quality by applying a classic Monte Carlo method to obtain the probability density functions of several output quantities. The effects of installation errors are also studied for a range of train speeds. Finally, the pre-sag that, on average, produces the best behaviour of the system is identified, allowing for the uncertainty in the catenary installation. The results obtained show the convenience to consider variability in pantograph-catenary dynamic simulations.The authors would like to acknowledge the financial support received from the FPU program offered by the Spanish Ministry of Education, Culture and Sports (Ministerio de Educacion, Cultura y Deportes) [grant number FPU13/04191]. The funding provided by the Regional Government of Valencia (Generalitat Valenciana) [PROMETEO/2016/007] and the Spanish Ministry of Economy, Industry and Competitiveness (Ministerio de Economia, Industria y Competitividad) [TRA2017-84736-R] is also acknowledged.Gregori Verdú, S.; Tur Valiente, M.; Tarancón Caro, JE.; Fuenmayor Fernández, F. (2019). Stochastic Monte Carlo simulations of the pantograph-catenary dynamic interaction to allow for uncertainties introduced during catenary installation. Vehicle System Dynamics. 57(4):471-492. https://doi.org/10.1080/00423114.2018.1473617S471492574Bruni, S., Ambrosio, J., Carnicero, A., Cho, Y. H., Finner, L., Ikeda, M., … Zhang, W. (2014). The results of the pantograph–catenary interaction benchmark. Vehicle System Dynamics, 53(3), 412-435. doi:10.1080/00423114.2014.953183Gregori, S., Tur, M., Nadal, E., & Fuenmayor, F. J. (2017). An approach to geometric optimisation of railway catenaries. Vehicle System Dynamics, 56(8), 1162-1186. doi:10.1080/00423114.2017.1407434Collina, A., & Bruni, S. (2002). Numerical Simulation of Pantograph-Overhead Equipment Interaction. Vehicle System Dynamics, 38(4), 261-291. doi:10.1076/vesd.38.4.261.8286Shabana, A. A. (1998). Nonlinear Dynamics, 16(3), 293-306. doi:10.1023/a:1008072517368Tur, M., García, E., Baeza, L., & Fuenmayor, F. J. (2014). A 3D absolute nodal coordinate finite element model to compute the initial configuration of a railway catenary. Engineering Structures, 71, 234-243. doi:10.1016/j.engstruct.2014.04.015Ambrósio, J., Pombo, J., Antunes, P., & Pereira, M. (2014). PantoCat statement of method. Vehicle System Dynamics, 53(3), 314-328. doi:10.1080/00423114.2014.969283Herrador, M. Á., Asuero, A. G., & González, A. G. (2005). Estimation of the uncertainty of indirect measurements from the propagation of distributions by using the Monte-Carlo method: An overview. Chemometrics and Intelligent Laboratory Systems, 79(1-2), 115-122. doi:10.1016/j.chemolab.2005.04.010Dudley, R. M. (1978). Central Limit Theorems for Empirical Measures. The Annals of Probability, 6(6), 899-929. doi:10.1214/aop/1176995384Bonett, D. G. (2006). Approximate confidence interval for standard deviation of nonnormal distributions. Computational Statistics & Data Analysis, 50(3), 775-782. doi:10.1016/j.csda.2004.10.003Efron, B., & Tibshirani, R. J. (1994). An Introduction to the Bootstrap. doi:10.1201/9780429246593Cho, Y. H., Lee, K., Park, Y., Kang, B., & Kim, K. (2010). Influence of contact wire pre-sag on the dynamics of pantograph–railway catenary. International Journal of Mechanical Sciences, 52(11), 1471-1490. doi:10.1016/j.ijmecsci.2010.04.00

A simulation study on some confidence intervals for the population standard deviation

In this paper a robust estimator against outliers along with some other existing interval estimators are considered for estimating the population standard deviation. An extensive simulation study has been conducted to compare and evaluate the performance of the interval estimators. The exact and the proposed robust method are easy to calculate and are not overly computer-intensive. It appears that the proposed robust method is performing better than other confidence intervals for estimating the population standard deviation, specifically in the presence of outliers and/or data are from a skewed distribution. Some real-life examples are considered to illustrate the application of the proposed confidence intervals, which also supported the simulation study to some extent

Confidence intervals for variance components and functions of variance components in the random effects model under non-normality

Methods for constructing confidence intervals for the variance components from a random effects model have important applications in a variety of disciplines. A fundamental analysis with random effects models is confidence intervals for the variance components or functions of the variance components. Many methods for constructing confidence intervals are currently being used. These methods work well under normality, equal variance, and equal sample size, but are very sensitive to any violations of these assumptions. This dissertation addresses the problem of constructing confidence intervals for variance components when the random effects or the errors are not normally distributed. The focus is on balanced one way random effects models and four parameters - the between group variance, the ratio of between to within group variance components, the intra-class correlation, and the ``stepped-up reliability - are examined. All of our proposed methods replace the usual estimate of the standard error calculated under the assumption of normality with an estimate calculated under non-normality. For the between group variance, this estimate includes an estimate of the kurtosis of the distribution of the random effect. For the other three parameters, the standard error estimate includes estimates of both the kurtosis of the distribution of the random effect and the kurtosis of the distribution of the errors. If the researcher does not have any information about the distribution of the random effects or the errors, a general kurtosis estimate is used which is based on Pearson\u27s kurtosis estimator, but with adjustments suggested by Bonett and Shoemaker. If it seems reasonable to assume the random effect or the errors follow a Beta or Gamma distribution, the kurtosis is estimated by first estimating the parameters of these distributions and then using the parameter estimates to estimate the kurtosis. If a previous study has been conducted, kurtosis estimates from the previous study can be pooled with the kurtosis estimates from the current study. Finally, if the researcher can theoretically specify a kurtosis value based on expert knowledge about their field of study, this specified kurtosis value can be used in place of an estimate. Our findings indicate that the proposed methods, especially those that incorporate a researcher\u27s knowledge about the distributions of the random effect and the errors, perform better than the current methods when the normality assumption is violated

Non-parametric statistical techniques for estimation of regression coefficients and coefficient of variation in corporate finance

Predmet istraživanja disertacije je intervalno ocenjivanje regresionih koeficijenata u prostom linearnom regresionom modelu i kvadratnom regresionom modelu ako slučajna greška nema normalnu raspodelu i intervalno ocenjivanje mera disperzije ako osnovni skup ne sledi normalnu raspodelu. Ako su narušene polazne pretpostavke, proporcija simuliranih intervala za regresione koeficijente i mere disperzije može znatno odstupati od nominalnog nivoa pouzdanosti. U radu su razvijene originalne metode za intervalno ocenjivanje regresionih koeficijenata u prostom linearnom i kvadratnom regresionom modelu zasnovane na Edgeworth-ovom razvoju raspodele t statistika koje se koriste u pomenutim modelima. Dalje, predložene su transformacije metoda koje se koriste za intervalno ocenjivanje koeficijenta varijacije. Reč je o transformaciji zasnovanoj na odsečenoj sredini i bootstrap transformaciji. Validnost predloženih metoda proverena je kroz simulacije koristeći različite raspodele, kao i podatke u oblasti korporativnih finansija. Korporativne finansije obuhvataju praćenje efekata finansiranja kako bi se maksimizirala vrednost kompanije, kao i različite aspekte značajne za rast kompanije. Iz tog razloga, predmet razmatranja prilikom konstrukcije intervalnih ocena bili su podaci o indikatoru verovatnoće bankrotstva, količniku ukupnog duga, meri sistematskog rizika i dividendama. Utvrđeno je da su, u većini razmatranih slučajeva, proporcije simuliranih intervala zasnovanih na predloženim metodama bliže nominalnom nivou pouzdanosti u poređenju sa proporcijama intervala proučavanih u literaturi. Na osnovu rezultata dobijenih u empirijskom delu, date su preporuke za intervalno ocenjivanje koje se mogu koristiti za donošenje pouzdanih zaključaka, pre svega, u oblasti korporativnih finansija. Ključne reči: proporcija simuliranih intervala poverenja, nominalni nivo pouzdanosti, regresioni koeficijent, prost linearni regresioni model, kvadratni regresioni model, koeficijent varijacije, Edgeworth-ov razvoj raspodele t statistike, odsečena sredina, korporativne finansije.The subject of the research of dissertation is the interval estimation of the regression coefficients in the simple linear regression model and quadratic regression model if an error term does not have normal distribution and interval estimation of the measures of dispersion if the population does not follow normal distribution. If the initial assumptions are violated, the proportion of the simulated intervals for the regression coefficients and measures of dispersion can noticeably deviate from the nominal confidence level. The original methods for the interval estimation of the regression coefficients in the simple linear and quadratic regression model, based on the Edgeworth's expansion of the distribution of the t statistics which are used in the mentioned models, were developed. Further, the transformations of the methods used for the interval estimation of the coefficient of variation were proposed. It is about the transformation based on the trimmed mean and the bootstrap transformation. The validation of the proposed methods was checked through simulations using different distributions, as well as the data in the field of corporate finance. Corporate finance includes monitoring the effects of financing in order to maximize a company’s value, as well as various aspects important to the company’s growth. For that reason, the data on the bankruptcy probability indicator, total debt ratio, systematic risk measure and dividends were considered in order to construct the interval estimates. It was found that, in most of the considered cases, the proportions of the simulated intervals based on the proposed methods are closer to the nominal confidence level compared with the proportions of the intervals studied so far in the literature. Based on the results obtained in the empirical part, the recommendations for the interval estimation, which can be used to draw the reliable conclusions, primarily, in the field of corporate finance, were given. Key words: proportion of the simulated confidence intervals, nominal confidence level, regression coefficient, simple linear regression model, quadratic regression model, coefficient of variation, Edgeworth's expansion of the distribution of the t statistic, trimmed mean, corporate finance