On functionals of order statistics期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

On functionals of order statistics

Authors:	Dr W Sendler

Institution:	(1) Dortmund;(2) Universität Trier, Fachbereich 4, Schneidershof, D-5500 Trier

Abstract:	Summary Let g_n be real functions,U _ni, 1in, the ordered sample ofn independentU(0,1) distributed random variables, andc _ni(), 1in, 01 be (known) real numbers,n=1, 2, ... The random quantity $T_n (\alpha ): = n^{ - 1} \sum\limits_{i = 1}^n {c_{ni} (\alpha )g_n (U_{ni} )}$ , 01, is studied. Based on a method proposed byShorack 1972] the main result is the weak convergence of $H_n : = n^{1/2} (T_n - \mu _n )$ to Gaussian processes, where $\mu _n (\alpha ): = \sum\limits_{i = 1}^n {c_{ni} (\alpha )} \int\limits_{(i - 1)/n}^{i/n} {g_n (t)dt}$ , 01. The convergence is with respect to theSkorokhod 1956]-topologiesM ₂,M ₁ onD (I) and the -topology onC(I), depending on the conditions imposed on thec _ni().

Keywords:
本文献已被 SpringerLink 等数据库收录！