Extension to higher dimensions of the Jaeschke-Eicker result on the standardized empirical process

被引：6

作者：

Einmahl, JHJ ^{[1
]}

机构：

[1] EINDHOVEN UNIV TECHNOL,DEPT MATH & COMP SCI,5600 MB EINDHOVEN,NETHERLANDS

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 1996年 / 25卷 / 04期

关键词：

asymptotic distribution; empirical process; heavy weights;

D O I：

10.1080/03610929608831733

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 asymptotic distribution of the sup-norm of the heavily weighted empirical process is established in the multidimensional case. This theorem extends in particular the famous result in Jaeschke (1975, 1979) to higher dimensions. There is a striking difference between the behaviour for higher dimensions and that for dimension one, especially the limiting distribution is now a simple transformation of a standard exponential random variable.

引用

页码：813 / 822

页数：10

共 6 条

[1] ASYMPTOTIC TAIL BEHAVIOR OF UNIFORM MULTIVARIATE EMPIRICAL PROCESSES [J].

CSORGO, M ;

HORVATH, L .

ANNALS OF PROBABILITY, 1990, 18 (04) :1723-1738

[2] ASYMPTOTIC-DISTRIBUTION OF THE SUPREMA OF THE STANDARDIZED EMPIRICAL PROCESSES [J].

EICKER, F .

ANNALS OF STATISTICS, 1979, 7 (01) :116-138

[3] ASYMPTOTIC-DISTRIBUTION OF THE SUPREMUM OF THE STANDARDIZED EMPIRICAL DISTRIBUTION FUNCTION ON SUB-INTERVALS [J].

JAESCHKE, D .

ANNALS OF STATISTICS, 1979, 7 (01) :108-115

[4]

JAESCHKE D, 1975, THESIS DORTMUND U

[5]

MASON DM, 1983, STOCHASTIC PROCESS A, V15, P99

[6]

[No title captured]

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