STRONG UNIFORM CONSISTENCY FOR RELATIVE ERROR OF THE REGRESSION FUNCTION ESTIMATOR FOR TRUNCATED-CENSORED DATA

Abstract - Survival analysis is the part of statistics, in which the variable of interest (lifetime) may often be interpreted as the time elapsed between two events and then, one may not be able to observe completely the variable under study. Such variables arise frequently in practice for life data, they are typically appearing in a medical or an engineering life test studies. Among the different forms in which incomplete data appear Left truncation and right censoring (LTRC), that means the target variable is not only censored from the right, but subject to left-truncation too. In the present work we built a newkernel estimate of the regression function based on the minimization of the mean squared relative error. Under classical conditions we establish the uniform almost sure convergence with rate over a compact set. To illustrate the good behavior of our estimator and to make some comparisons with the classical estimator of regression function a simulation studies was carried out for different combinations of the sample size n, the truncation rate and the censoring rate, in the cases of one- and bi-dimensional covariate. BIOGRAPHY [1] Gijbels, I., Wang, J. L. (1993). Strong representations of the survival function estimator for truncated and censored data with applications. J. Multivar. Anal. 47 :210–229. [2] Park, H. and Stefanski, L.A. (1998). Relative-error prediction. Statist. Probab. Lett 40 : 227-236. [3] Tsai, W. Y., and Jewell, N. P., Wang, M. C. (1987). A note on the product-limit estimator under right censoring and left truncation. Biometrika 74 :883-886.