Strong Convergence Rates of Wavelet Estimators in Semiparametric Regression Models with Censored Data*

ABSTRACT

The paper studies a semiparametric regression model

Y_i = X_iβ + g(T_i ) + e_i , i = 1,2,L,n .

where Y_i is censored on the right by another random variable C_i with known or unknown distribution G . Firstly, the wavelet estimators of parameter β and nonparameter g(t) are given by wavelet smoothing and the synthetic data methods. Secondly, under general conditions, the laws of the iterated logarithm for the wavelet estimators of parameter and strong uniform convergence rates for the wavelet estimators of nonparameter are investigated. Lastly, the validity of method is illuminated by the simulation example.

Keywords:

Semiparametric regression model, Wavelet estimate, Censored data, Law of the iterated logarithm, Strong uniform convergence rate.