NONPARAMETRIC ESTIMATION OF HAZARD FUNCTIONS AND THEIR DERIVATIVES UNDER TRUNCATION MODEL

ÜLKÜ GÜRLER^{1} AND JANE-LING WANG^{2}

1Bilkent University, Faculty of Industrial Engineering, Ankara, Turkey 2Division of Statistics, University of California, Davis, CA 95616-8705, U.S.A.

(Received August 26, 1991; revised September 16, 1992)

Abstract. Nonparametric kernel estimators for hazard functions and their derivatives are considered under the random left truncation model. The estimator is of the form of sum of identically distributed but dependent random variables. Exact and asymptotic expressions for the biases and variances of the estimators are derived. Mean square consistency and local asymptotic normality of the estimators are established. Adaptive local bandwidths are obtained by estimating the optimal bandwidths consistently.

Key words and phrases: Adaptive bandwidth choice, consistency, Hájek projection, kernel estimate, mean square error, tightness.