UNIFORM STRONG CONSISTENT ESTIMATION OF AN IFRA DISTRIBUTION FUNCTION

[摘要] Let F(n)BAR be an estimator of an IFRA survival function FBAR and let A be such that 0 < F(A)BAR) < 1. The main result constructs an IFRA estimator by splicing the smallest increasing failure rate on the average majorant and greatest increasing failure rate on the average minorant of the restrictions of F(n)BAR to the intervals [0, A] and [A, infinity), respectively. The resulting etimator F(n)BAR has the property that sup(x) \F(n)BAR - FBAR\ less-than-or-equal-to k sup(x) \F(n)BAR - FBAR\ where k greater-than-or-equal-to 2, and k = 2 if and only if A is the median of F. As a consequence, if F(n)BAR represents the empirical survival function, or the Kaplan-Meier estimator, the estimator F(n)BAR inherits the strong and uniform convergence properties, as well as the optimal rates of convergence of the empirical survival function and Kaplan-Meier estimator respectively. Simulations show a substantial improvement in mean-squared error when comparing F(n)BAR to those IFRA estimators available in the literature. Under suitable conditions, asymptotic confidence intervals for F(t0)BAR are also provided. (C) 1994 Academic Press, Inc.

[发布日期] 1994-04-01

[关键词] HAZARD FUNCTION;TAILS OF DISTRIBUTIONS;REGULARLY VARYING TAILS;KAPLAN-MEIER ESTIMATOR;CENSORING;SIFRAM;GIFRAM