A Review of Kernel Density Estimation with Applications to Econometrics

Nonparametric density estimation is of great importance when econometricians want to model the probabilistic or stochastic structure of a data set. This comprehensive review summarizes the most important theoretical aspects of kernel density estimation and provides an extensive description of classical and modern data analytic methods to compute the smoothing parameter. Throughout the text, several references can be found to the most up-to-date and cut point research approaches in this area, while econometric data sets are analyzed as examples. Lastly, we present SIZer, a new approach introduced by Chaudhuri and Marron (2000), whose objective is to analyze the visible features representing important underlying structures for different bandwidths

A Comparative Study of Additive and Nonparametric Regression Estimators and Variable Selection Procedures

One of the biggest challenges in nonparametric regression is the curse of dimensionality. Additive models are known to overcome this problem by estimating only the individual additive effects of each covariate. However, if the model is misspecified, the accuracy of the estimator compared to the fully nonparametric one is unknown. In this work the efficiency of completely nonparametric regression estimators such as the Loess is compared to the estimators that assume additivity in several situations, including additive and non-additive regression scenarios. The comparison is done by computing the oracle mean square error of the estimators with regards to the true nonparametric regression function. Then, a backward elimination selection procedure based on the Akaike Information Criteria is proposed, which is computed from either the additive or the nonparametric model. Simulations show that if the additive model is misspecified, the percentage of time it fails to select important variables can be higher than that of the fully nonparametric approach. A dimension reduction step is included when nonparametric estimator cannot be computed due to the curse of dimensionality. Finally, the Boston housing dataset is analyzed using the proposed backward elimination procedure and the selected variables are identified

Monte carlo algorithm for trajectory optimization based on markovian readings

This paper describes an efficient algorithm to find a smooth trajectory joining two points A and B with minimum length constrained to avoid fixed subsets. The basic assumption is that the locations of the obstacles are measured several times through a mechanism that corrects the sensors at each reading using the previous observation. The proposed algorithm is based on the penalized nonparametric method previously introduced that uses confidence ellipses as a fattening of the avoidance set. In this paper we obtain consistent estimates of the best trajectory using Monte Carlo construction of the confidence ellipse. © Springer Science+Business Media, LLC 2010.This paper describes an efficient algorithm to find a smooth trajectory joining two points A and B with minimum length constrained to avoid fixed subsets. The basic assumption is that the locations of the obstacles are measured several times through a mec511305321CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO475504/2008-9; 301542/2007-4; 301530/2007-62006/02095-5Asseo, S.J., In-flight replanning of penetration routes to avoid threat zones of circular shapes (1998) Aerospace and Electronics Conference, 1998, pp. 383-391. , NAECON 1998. Proceedings of the IEEE 1998 NationalAström, K.J., Murray, R.M., (2008) Feedback Systems: An Introduction for Scientists and Engineers, , Princeton University Press, PrincetonAyache, N., Faugeras, O.D., Building, registrating, and fusing noisy visual maps (1988) Int. J. Robot. Res., 7 (6), pp. 45-65Azarbayejani, A., Pentland, A.P., Recursive estimation of motion, structure, and focal length (1995) IEEE Trans. Pattern Anal. Mach. Intell., 17, pp. 562-575Barraquand, J., Latombe, J.-C., Nonholonomic multibody mobile robots: Controllability and motion planning in the presence of obstacles (1993) Algorithmica, 10 (2-4), pp. 121-155. , Computational robotics: the geometric theory of manipulation, planning, and controlBetts, J.T., Survey of numerical methods for trajectory optimization (1998) Journal of Guidance, Control, and Dynamics, 21 (2), pp. 193-207Brockwell, P.J., Davis, R.A., (1996) Introduction to Time Series and Forecasting, , Peter J. Brockwell and Richard A. Davis. Springer, New YorkBroida Ted, J., Chandrashekhar, S., Chellappa Rama, Recursive 3-D motion estimation from a monocular image sequence (1990) IEEE Transactions on Aerospace and Electronic Systems, 26 (4), pp. 639-656. , DOI 10.1109/7.55557Chapuis, R., Aufrere, R., Chausse, F., Accurate road following and reconstruction by computer vision (2002) IEEE Transactions on Intelligent Transportation Systems, 3 (4), pp. 261-270. , DOI 10.1109/TITS.2002.804751Choset, H., Lynch, K., Hutchinson, S., Kantor, G., Burgardand, W., Kavraki, L., Thrun, S., (2005) Principles of Robot Motion: Theory, Algorithms and Implementations, , MIT Press, CambridgeDias, R., Garcia, N.L., Zambom, A.Z., A penalized nonparametric method for nonlinear constrained optimization based on noisy data (2008) Comput. Optim. Appl., , doi:10.1007/s10589-008-9185-6Fliess, M., Levine, J., Martin, P., Rouchon, P., On differentially flat nonlinear-systems (1992) C. R. Acad. Sci., Ser. 1 Math., 315 (5), pp. 619-624Fliess, M., Lévine, J., Rouchon, P., Flatness and defect of nonlinear systems: Introductory theory and examples (1995) Int. J. Control, 61, pp. 1327-1361Grundel, D., Murphey, R., Pardalos, P., Prokopyev, O., Cooperative systems, control and optimization (2007) Lecture Notes in Economics and Mathematical Systems, 588. , Springer, BerlinHarvey, A.C., (1990) Forecasting, Structural Time Series Models and the Kalman Filter, , Cambridge University Press, CambridgeHirsch, M.J., Pardalos, P., Murphey, R., Grundel, D., Advances in cooperative control and optimization (2007) Lecture Notes in Control and Information Sciences, 369. , Springer, Berlin Papers from a meeting held in Gainesville, FL, January 31-February 2Laumond, J.-P., Robot motion planning and control (1998) Lecture Notes in Control and Information Science, 229. , http://www.laas.fr/jpl/book.html, Springer, Berlin onlineLavalle, S., (2006) Planning Algorithms, , Cambridge University Press, CambridgeMatthies, L., Kanade, T., Szeliski, R., (1989) Kalman Filter-based Algorithms for Estimating Depth from Image SequencesPerrollaz, M., Labayrade, R., Gallen, R., Aubert, D., A three resolution framework for reliable road obstacle detection using stereovision (2007) MVA, pp. 469-472Tiwari, A., Chandra, H., Yadegar, J., Wang, J., Constructing optimal cyclic tours for planar exploration and obstacle avoidance: A graph theory approach (2007) Advances in Variable Structure and Sliding Mode Control, , Springer, Berli

Consistent variable selection for functional regression models

CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL E NÍVEL SUPERIORThe dual problem of testing the predictive significance of a particular covariate, and identification of the set of relevant covariates is common in applied research and methodological investigations. To study this problem in the context of functional linear regression models with predictor variables observed over a grid and a scalar response, we consider basis expansions of the functional covariates and apply the likelihood ratio test. Based on p-values from testing each predictor, we propose a new variable selection method, which is consistent in selecting the relevant predictors from set of available predictors that is allowed to grow with the sample size n. Numerical simulations suggest that the proposed variable selection procedure outperforms existing methods found in the literature. A real dataset from weather stations in Japan is analyzed. (C) 2016 Published by Elsevier Inc.The dual problem of testing the predictive significance of a particular covariate, and identification of the set of relevant covariates is common in applied research and methodological investigations. To study this problem in the context of functional linear regression models with predictor variables observed over a grid and a scalar response, we consider basis expansions of the functional covariates and apply the likelihood ratio test. Based on p-values from testing each predictor, we propose a new variable selection method, which is consistent in selecting the relevant predictors from set of available predictors that is allowed to grow with the sample size n. Numerical simulations suggest that the proposed variable selection procedure outperforms existing methods found in the literature. A real dataset from weather stations in Japan is analyzed.1466371CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL E NÍVEL SUPERIORCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL E NÍVEL SUPERIOR302956/2013-12013/07375-0; 2013/00506-1sem informaçã

A penalized nonparametric method for nonlinear constrained optimization based on noisy data

Autonomous vehicle, B-splines, Consistent estimator, Confidence ellipses, Constrained optimization, Nonparametric method,