QUADRATIC ERROR OF THE ESTIMATION OF THE HAZARD FUNCTION CONDITIONAL IN NONPARAMETRIC FUNCTIONAL MODEL

Yıl 2015, Cilt: 8 Sayı: 1, 1 - 14, 01.03.2015

Naouel Belkhir Abbes Rabhi Sara Soltani.

Öz

This paper deals with a scalar response conditioned by a functional random variable. The maingoal is to estimate nonparametrically Kernel type estimator for the conditional hazard function. Finally,asymptotic properties of this estimator are stated bias the exact expression involved in the leading terms ofthe quadratic error

Anahtar Kelimeler

Functional data, Kernel conditional hazard function, Kernel estimation, NonparametricEstimation, Probabilities of small balls

Kaynakça

• Bosq, D. and Lecoutre, J. P.,(1987). Thorie de l’estimation fonctionnelle Ed. Economica.
• Dabo-Niang, S., (2002). Estimation de la densit dans un espace de dimension inŞnie : application aux diffusions, C. R., Math., Acad. Sci. Paris, 334, 213-216.
• Dabo-Niang, S., (2002). Sur l’estimation fonctionnelle en dimension inŞnie : Application aux diffusions,
• Thse de Doctorat, Universit de Paris 6. Ferraty, F., Rabhi, A., Vieu P., (2005). Conditional Quantiles for Dependent Functional Data with
• Application to the Climatic El N¨ıno Phenomenon. Sankhy¨a, 67, 378-398. Ferraty, F. and Vieu, P., (2006). Nonparametric Functional Data Analysis. Theory and Practice,Springer
• Series in Statistics. Springer, New York. Ferraty, F., A., Rabhi, Vieu,P., (2008). Estimation nonparamtrique de la fonction de hasard avec vari- ables explicatives fonctionnelles, Revue Roumaine de mathmatique.
• Gasser, T. and Hall, P.,Presnell, B., (1998). Nonparametric estimation of the mode of a distribution of random curves, Journal of the Royal Statistical Society, Ser. B., 60, 681-691.
• Gefeller, O. and Michels, P., (1992). A review on smoothing methods for the estimation of the hazard rate based on kernel functions, In Y. Dodge and J. Whittaker (Eds), Computational Statistics, Physica- Verlag, 459-464.
• Hassani, S., Sarda, P., Vieu, P., (1986). Approche non-paramtrique en thorie de la Şabilit: revue bibli- ographique, Rev. Statist. Appl., 35, 27-41.
• Izenman, A. , (1991). Developments in nonparametric density estimation, J. Amer. Statist. Assoc., 86, 224.
• Pascu, M. , Vaduva, M., Vaduva I., (2003). Nonparametric estimation of the hazard rate: a survey, Rev.
• Roumaine Math. Pures Appl., 48, 173-191. Patil, P.N., Wells, M.T., Maron, J.S., (1994). Some heuristics of kernel based estimators of ratio func- tions, J. Nonparametr. Statist., 4, 203-209.
• Ramsay, J. and Silverman, B., (2005). Functional Data Analysis, 2nd Ed., Springer Series in Statistics. Springer, New York.
• Sarda, P. and Vieu, P., (2000). Kernel regression. In: M. Schimek (ed.), Smoothing and regression.
• Approaches, computation and application, Wiley Series in Probability and Statistics, Wiley, New York, 70. Singpurwalla, N. and Wong, M.Y., (1983). Estimation of the failure rate - a survey of nonparametric models. Part I: Non-Bayesian methods, Comm. Statist. Theory Methods, 12, 559-588.
• Troutman, J. L., (1996). Variatonal Calculus and Optimal Control, Springer-Verlag.
• Vieu, P., (1991). Quadratic errors for nonparametric estimates under dependence, J.Multivariate Anal., ,324-347.