Distributional expansions of powered order statistics from general error distribution

Abstract

Let $\{X_n,n\ge 1\}$ be a sequence of independent random variables with common general error distribution $GED(v)$ with shape parameter $v>0$, and let $M_{n,r}$ denote the $r$th largest order statistics of $X_1,X_2,\cdots ,X_n$. With different normalizing constants the distributional expansions of normalized powered order statistics $|M_{n,r}{|}^p$ are established, from which the convergence rates of powered order statistics to their limits are derived. This paper generalized Hall's results on powered-extremes of normal sequence.

18 pages