Limit theorems for empirical processes based on dependent data

被引：15

作者：

Berti, Patrizia ^{[1
]}

Pratelli, Luca ^{[2
]}

Rigo, Pietro ^{[3
]}

机构：

[1] Univ Modena & Reggio Emilia, Modena, Italy

[2] Accademia Navale Livorno, Livorno, Italy

[3] Univ Pavia, I-27100 Pavia, Italy

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2012年 / 17卷

关键词：

Conditional identity in distribution; Empirical process; Exchangeability; Predictive measure; Stable convergence; PREDICTIVE-DISTRIBUTIONS; RANDOM-VARIABLES; CONVERGENCE; SEQUENCES;

D O I：

10.1214/EJP.v17-1765

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let (X-n) be any sequence of random variables adapted to a filtration (G(n)). Define a(n)(.) = P(Xn+1 is an element of . vertical bar G(n)), b(n) = 1/n Sigma(n-1)(i=0) a(i), and mu(n) = 1/n Sigma(n)(i=1) delta(Xi). Convergence in distribution of the empirical processes B-n = root n (mu(n) - b(n)) and C-n = root n (mu(n) - a(n)) is investigated under uniform distance. If (X-n) is conditionally identically distributed, convergence of B-n and C-n is studied according to Meyer-Zheng as well. Some CLTs, both uniform and non uniform, are proved. In addition, various examples and a characterization of conditionally identically distributed sequences are given.

引用

页码：1 / 18

页数：18

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