WEAK-CONVERGENCE FOR RECTANGLES-INDEXED WEIGHTED EMPIRICAL U-STATISTIC UNDER MIXING CONDITIONS

被引：0

作者：

RAGBI, B ^{[1
]}

机构：

[1] CNRS,URA 0745,F-31062 TOULOUSE,FRANCE

来源：

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE | 1995年 / 320卷 / 07期

关键词：

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We have established in [3] the weak convergence of the weighted multivariate empirical U-statistic indexed by points under mixing conditions. In this paper we extend these results to the convergence of the weighted empirical U-statistic indexed by rectangles of [0, 1](p) with respect to the Skorohod topology in (D) over bar(p) space of functions indexed by rectangles introduced by Harel and Puri [2]. Applications to Cramer-Von Mises type and Anderson-Darling type statistics are given.

引用

页码：871 / 874

页数：4

共 36 条

[1] THE SPACE DK AND WEAK-CONVERGENCE FOR RECTANGLES-INDEXED PROCESSES UNDER MIXING CONDITIONS
HAREL, M
PURI, M
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1988, 306 (04): : 207 - 210
[2] Weak convergence for rectangle-indexed weighted multivariate empirical U-statistic processes under mixing conditions
Ragbi, B
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 221 (02) : 476 - 498
[3] WEAK-CONVERGENCE OF THE WEIGHTED EMPIRICAL PROCESS INDEXED BY RECTANGLES UNDER MIXING CONDITION
HAREL, M
PURI, M
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1987, 26 (02) : 210 - 211
[4] WEAK-CONVERGENCE AND GLIVENKO CANTELLI RESULTS FOR EMPIRICAL PROCESSES OF U-STATISTIC STRUCTURE
SCHNEEMEIER, W
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1989, 33 (02) : 325 - 334
[5] WEAK-CONVERGENCE OF WEIGHTED MULTIVARIATE EMPIRICAL PROCESSES UNDER MIXING CONDITIONS
HAREL, M
PURI, M
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1987, 305 (03): : 93 - 95
[6] WEAK CONVERGENCE OF U-STATISTIC PROCESSES, AND OF EMPIRICAL PROCESS
LOYNES, RM
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1978, 83 (MAR) : 269 - 272
[7] WEAK-CONVERGENCE OF THE SIMPLE LINEAR RANK-STATISTIC UNDER MIXING CONDITIONS IN THE NONSTATIONARY CASE
HAREL, M
PURI, ML
THEORY OF PROBABILITY AND ITS APPLICATIONS, 1993, 38 (03) : 405 - 422
[8] WEAK-CONVERGENCE OF THE U-STATISTIC AND WEAK INVARIANCE OF THE ONE-SAMPLE RANK ORDER STATISTIC FOR MARKOV-PROCESSES AND ARMA MODELS
HAREL, M
PURI, ML
JOURNAL OF MULTIVARIATE ANALYSIS, 1989, 31 (02) : 258 - 265
[9] THE SPACE DK LAND WEAK-CONVERGENCE FOR THE RECTANGLE-INDEXED PROCESSES UNDER MIXING
HAREL, M
PURI, ML
ADVANCES IN APPLIED MATHEMATICS, 1990, 11 (04) : 443 - 474
[10] WEAK-CONVERGENCE OF THE SERIAL LINEAR RANK-STATISTIC WITH UNBOUNDED SCORES AND REGRESSION CONSTANTS UNDER MIXING CONDITIONS
HAREL, M
PURI, M
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1988, 307 (11): : 617 - 620

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