On Kernel Hazard Rate Function Estimate for Associated and Left Truncated Data

Abstract

Let {XN , N ≥ 1} be a sequence of strictly stationary associated random variables of interest, and {TN , N ≥ 1} be a sequence of random truncating variables assumed to be independent from {XN , N ≥ 1}. In this paper, we establish the strong uniform consistency with a rate of a kernel hazard rate function estimator, when the variable of interest is subject to random left truncation under association condition. Simulation results are also provided to evaluate the finite-sample performances of the proposed estimator.

Keywords

• associated data
• hazard rate function
• Lynden-Bell estimator
• random left truncation
• strong uniform consistency rate