Density and Hazard Rate Estimation for Censored and A-Mixing Data Using Gamma Kernels

CORE Discussion Paper 2006/118

22 Pages Posted: 14 Mar 2007

See all articles by Taoufik Bouezmarni

Taoufik Bouezmarni

HEC Montreal

J. V. K. Rombouts

HEC Montreal; Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE); Centre interuniversitaire sur le risque, les politiques économiques et l'emploi (CIRPÉE); Center for Interuniversity Research and Analysis on Organization (CIRANO)

Date Written: December 2006

Abstract

In this paper we consider the nonparametric estimation for a density and hazard rate function for right censored α-mixing survival time data using kernel smoothing techniques. Since survival times are positive with potentially a high concentration at zero, one has to take into account the bias problems when the functions are estimated in the boundary region. In this paper, gamma kernel estimators of the density and the hazard rate function are proposed. The estimators use adaptive weights depending on the point in which we estimate the function, and they are robust to the boundary bias problem. For both estimators, the mean squared error properties, including the rate of convergence, the almost sure consistency and the asymptotic normality are investigated. The results of a simulation demonstrate the excellent performance of the proposed estimators.

Keywords: Gamma kernel, Kaplan Meier, density and hazard function, mean integrated squared error, consistency, asymptotic normality

Suggested Citation

Bouezmarni, Taoufik and Rombouts, Jeroen, Density and Hazard Rate Estimation for Censored and A-Mixing Data Using Gamma Kernels (December 2006). CORE Discussion Paper 2006/118, Available at SSRN: https://ssrn.com/abstract=970914 or http://dx.doi.org/10.2139/ssrn.970914

Taoufik Bouezmarni (Contact Author)

HEC Montreal ( email )

3000, Chemin de la Côte-Sainte-Catherine
Montreal, Quebec H2X 2L3
Canada

Jeroen Rombouts

HEC Montreal ( email )

3000, Chemin de la Côte-Sainte-Catherine
Montreal, Quebec H3T 2A7
Canada

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
B-1348 Louvain-la-Neuve, b-1348
Belgium

Centre interuniversitaire sur le risque, les politiques économiques et l'emploi (CIRPÉE) ( email )

Pavillon De Sève
Ste-Foy, Quebec G1K 7P4
Canada

Center for Interuniversity Research and Analysis on Organization (CIRANO) ( email )

2020 rue University, 25th floor
Montreal H3C 3J7, Quebec
Canada

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