Weak convergence in Lp(0, 1) of the uniform empirical process under dependence

被引：7

作者：

Oliveira, PE

Suquet, C

机构：

[1] Univ Coimbra, Dept Math, CMUC, P-3000 Coimbra, Portugal

[2] Univ Sci & Technol Lille, Lille, France

来源：

STATISTICS & PROBABILITY LETTERS | 1998年 / 39卷 / 04期

关键词：

association; empirical process; strong mixing; tightness;

D O I：

10.1016/S0167-7152(98)00091-1

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：

The weak convergence of the empirical process of strong mixing or associated random variables is studied in L-p(0, 1). We find minimal rates of convergence to zero of the mixing coefficients or the covariances, in either case, supposing stationarity of the underlying variables. The rates obtained improve, for p not too large, the corresponding results in the classical D(0, 1) framework. (C) 1998 Elsevier Science B.V. All rights reserved.

引用

页码：363 / 370

页数：8

共 50 条

[1] A weak convergence result for sequential empirical processes under weak dependence
Mohr, Maria
[J]. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2020, 92 (01) : 140 - 164
[2] EMPIRICAL PROCESS UNDER DEPENDENCE IN L(2)[0,1]
OLIVEIRA, PE
SUQUET, C
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1995, 321 (07): : 939 - 944
[3] WEAK-CONVERGENCE OF THE WEIGHTED EMPIRICAL QUANTILE PROCESS IN L2(0,1)
MASON, DM
[J]. ANNALS OF PROBABILITY, 1984, 12 (01): : 243 - 255
[4] Weak convergence of the empirical process of intermittent maps in L2 under long-range dependence
Dedecker, Jerome
Dehling, Herold
Taqqu, Murad S.
[J]. STOCHASTICS AND DYNAMICS, 2015, 15 (02)
[5] Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions
Chen, Xiaohong
Christensen, Timothy M.
[J]. JOURNAL OF ECONOMETRICS, 2015, 188 (02) : 447 - 465
[6] A Note on Weak Convergence of the Sequential Multivariate Empirical Process Under Strong Mixing
Axel Bücher
[J]. Journal of Theoretical Probability, 2015, 28 : 1028 - 1037
[7] A Note on Weak Convergence of the Sequential Multivariate Empirical Process Under Strong Mixing
Buecher, Axel
[J]. JOURNAL OF THEORETICAL PROBABILITY, 2015, 28 (03) : 1028 - 1037
[8] Moment convergence rates for the uniform empirical process and the uniform sample quantile process
Chen, Youyou
Li, Tailong
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2017, 46 (18) : 9086 - 9091
[9] Weak hlder convergence of smoothed uniform quantile process
Hamadouche, D.
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2008, 37 (10) : 1497 - 1505
[10] WHEN UNIFORM WEAK CONVERGENCE FAILS: EMPIRICAL PROCESSES FOR DEPENDENCE FUNCTIONS AND RESIDUALS VIA EPI- AND HYPOGRAPHS
Buecher, Axel
Segers, Johan
Volgushev, Stanislav
[J]. ANNALS OF STATISTICS, 2014, 42 (04): : 1598 - 1634

← 1 2 3 4 5 →