Limit theorems for empirical processes based on dependent data

被引：14

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

共 50 条

[1] Limit theorems for smoothed empirical processes
Rost, D
[J]. HIGH DIMENSIONAL PROBABILITY II, 2000, 47 : 107 - 113
[2] Ratio limit theorems for empirical processes
Giné, E
Koltchinskii, V
Wellner, JA
[J]. STOCHASTIC INEQUALITIES AND APPLICATIONS, 2003, 56 : 249 - 278
[3] LIMIT-THEOREMS FOR EMPIRICAL PROCESSES
POLLARD, D
[J]. ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1981, 57 (02): : 181 - 195
[4] SOME LIMIT-THEOREMS FOR EMPIRICAL PROCESSES
GINE, E
ZINN, J
[J]. ANNALS OF PROBABILITY, 1984, 12 (04): : 929 - 989
[5] LIMIT THEOREMS FOR EMPIRICAL PROCESSES OF CLUSTER FUNCTIONALS
Drees, Holger
Rootzen, Holger
[J]. ANNALS OF STATISTICS, 2010, 38 (04): : 2145 - 2186
[6] Limit Theorems for Occupation Rates of Local Empirical Processes
Varron D.
[J]. Sankhya A, 2015, 77 (2): : 249 - 276
[7] A NOTE ON LIMIT-THEOREMS FOR PERTURBED EMPIRICAL PROCESSES
YUKICH, JE
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1989, 33 (01) : 163 - 173
[8] UNIFORM RATIO LIMIT-THEOREMS FOR EMPIRICAL PROCESSES
POLLARD, D
[J]. SCANDINAVIAN JOURNAL OF STATISTICS, 1995, 22 (03) : 271 - 278
[9] SOME LIMIT-THEOREMS FOR EMPIRICAL PROCESSES - DISCUSSION
ALEXANDER, KS
DUDLEY, RM
GAENSSLER, P
PHILIPP, W
POLLARD, D
PYKE, R
STUTE, W
[J]. ANNALS OF PROBABILITY, 1984, 12 (04): : 990 - 998
[10] Limit Theorems for Occupation Rates of Local Empirical Processes
Varron, Davit
[J]. SANKHYA-SERIES A-MATHEMATICAL STATISTICS AND PROBABILITY, 2015, 77 (02): : 249 - 276

← 1 2 3 4 5 →