LARGE DEVIATIONS FOR QUASI-ARITHMETICALLY SELF-NORMALIZED RANDOM VARIABLES

被引：0

作者：

Aubry, Jean-Marie ^{[1
]}

Zani, Marguerite ^{[1
]}

机构：

[1] Univ Paris Est Creteil, Lab Anal & Math Appl, CNRS, UMR 8050, F-94010 Creteil, France

来源：

ESAIM-PROBABILITY AND STATISTICS | 2013年 / 17卷

关键词：

Large deviations; self-normalised statistics; Bahadur exact slope;

D O I：

10.1051/ps/2011112

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：

We introduce a family of convex (concave) functions called sup (inf) of powers, which are used as generator functions for a special type of quasi-arithmetic means. Using these means, we generalize the large deviation result on self-normalized statistics that was obtained in the homogeneous case by [Q.-M. Shao, Self-normalized large deviations. Ann. Probab. 25 (1997) 285-328]. Furthermore, in the homogenous case, we derive the Bahadur exact slope for tests using self-normalized statistics.

引用

页码：1 / 12

页数：12

共 17 条

[1]

[Anonymous], RENDICONTI ACCADEMIA

[2]

[Anonymous], 1995, ASYMPTOTIC EFFICIENC

[3]

Bahadur R.R., 1971, APPL MATH

[4] A MEASURE OF ASYMPTOTIC EFFICIENCY FOR TESTS OF A HYPOTHESIS BASED ON THE SUM OF OBSERVATIONS [J].

CHERNOFF, H .

ANNALS OF MATHEMATICAL STATISTICS, 1952, 23 (04) :493-507

[5]

Cuvelier E., 2007, RECENT ADV STOCHASTI, P2

[6] Parametric families of probability distributions for functional data using Quasi-arithmetic means with Archimedean generators [J].

Cuvelier, Etienne ;

Noirhomme-Fraiture, Monique .

FUNCTIONAL AND OPERATORIAL STATISTICS, 2008, :127-133

[7]

de la Pena V.H., 2009, PROBAB APPL NER YORK

[8] Large and moderate diviations for Hotelling's T2-statistic [J].

Dembo, Amir ;

Shao, Qi-Man .

ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2006, 11 :149-159

[9]

Hardy Godfrey Harold, 1952, Inequalities, V2nd

[10]

Lai T.L., 2008, ADV LECT MATH ALM, V2, P3

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