Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series A, Pt. 3, 398--421

BERRY-ESSÉEN BOUND FOR PARAMETRIC ESTIMATE IN PARTIAL LINEAR MODEL WITH CENSORED DATA

By

GENGSHENG QIN, Hong Kong University of Science and Technology

and

BING-YI JING, Hong Kong University of Science and Technology

SUMMARY. Consider the semiparametric regression model Y=Xtb+g(T)+e, where b is a p x 1 unknown parameter vector, g is an unknown smooth function on [0,1], and e is an unobserved error. When observations are subject to random censorship, Qin (1995a,b) has constructed the estimator for b by the so-called synthetic data method. The asymptotic normality of the estimator was provided by Qin and Jing (1999). The purpose of this paper is to study the Berry-Esséen bound for the convergence rate to normality.

AMS (1991) subject classification. Primary 62G07, 62J05. secondary 62F12, 62G20.

Key words and phrases. Partial linear model; censored data; synthetic data; kernel method; Berry-Esséen bound.

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