Approximation to the expectation of a function of order statistics and its applications |
| |
Authors: | Shihong Cheng |
| |
Institution: | (1) Institute of Mathematics, Peking University, 100871 Beijing, China |
| |
Abstract: | Let {U
n
,n1} be a sequence of i.i.d. random variables uniformly distributed on the interval (0,1). For eachn1, denote the order statistics ofU
1,,U
n
byU
n,1U
n,n
. Under very general conditions on the ranksk
n,1,,k
n,m
, we give an approximation to
for anym-dimensional bounded and Borel measurable functiong. The approximation provides a unified approach to asymptotic distributions of a wide variety of order statistics, including the trimmed sums,U-statistics based on trimmed samples and the estimators for the index of an extreme value distribution. As the first applications, we discuss the central limit theorems for the so-called generalized Pickands' estimator and generalized moment estimator.This project is supported by the National Natural Science Foundation of China and Doctoral Program Foundation of Higher Education. |
| |
Keywords: | Uniform distribution order statistics approximation extreme value distribution asymptotic normality |
本文献已被 CNKI SpringerLink 等数据库收录! |
|