Distributions of exact tests in the exponential family

被引：29

作者：

Stehlik, M ^{[1
]}

机构：

[1] Comenius Univ, Fac Math Phys & Informat, Dept Probabil & Stat, Bratislava 84248, Slovakia

来源：

METRIKA | 2003年 / 57卷 / 02期

关键词：

exponential family; I-divergence; model testing; maximum likelihood; asymptotic efficiency; exact slopes; generalized linear models; Lambert W function;

D O I：

10.1007/s001840200206

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 aim of this paper is to give some results on the exact density of the I-divergence in the exponential family with gamma distributed observations. It is shown in particular that the I-divergence can be decomposed as a sum of two independent variables with known distributions. Since the considered I-divergence is related to the likelihood ratio statistics, we apply the method to compute the exact distribution of the likelihood ratio tests and discuss the optimality of such exact tests. One of these tests is the exact LR test of the model which is asymptotically optimal in the Bahadur sense. Numerical examples are provided to illustrate the methods discussed.

引用

页码：145 / 164

页数：20

共 50 条

[1] Distributions of exact tests in the exponential family
Milan Stehlík
Metrika, 2003, 57 : 145 - 164
[2] Exact distributions of tests of outliers for exponential samples
Nirpeksh Kumar
Statistical Papers, 2019, 60 : 2031 - 2061
[3] Exact distributions of tests of outliers for exponential samples
Kumar, Nirpeksh
STATISTICAL PAPERS, 2019, 60 (06) : 2031 - 2061
[4] ASYMPTOTIC HOMOGENEITY TESTS FOR MEAN EXPONENTIAL FAMILY DISTRIBUTIONS
SHANMUGAM, R
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1989, 23 (02) : 227 - 241
[5] Exact tests for exponential regression
Davidov, O
Zelen, M
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2000, 88 (01) : 87 - 97
[6] COMPOUND DISTRIBUTIONS OF INFINITELY DIVISIBLE DISTRIBUTIONS WITH EXPONENTIAL FAMILY AND WITH EXPONENTIAL TYPE FAMILY
PATIL, SA
ANNALS OF MATHEMATICAL STATISTICS, 1966, 37 (02): : 543 - &
[7] Exact distributions of XY for some bivariate exponential distributions
Nadarajah, Saralees
STATISTICS, 2006, 40 (04) : 307 - 324
[8] EXACT FORMULAE IN SEQUENTIAL ANALYSIS FOR EXPONENTIAL DISTRIBUTIONS
KEMPERMAN, JHB
ANNALS OF MATHEMATICAL STATISTICS, 1952, 23 (02): : 302 - 302
[9] EXACT TESTS FOR CENSORED EXPONENTIAL SURVIVAL DATA
BAUER, M
WILLIAMS, JS
BIOMETRICS, 1977, 33 (03) : 577 - 577
[10] A Family of Exact Goodness-of-Fit Tests for High-Dimensional Discrete Distributions
Saad, Feras A.
Freer, Cameron E.
Ackerman, Nathanael L.
Mansinghka, Vikash K.
22ND INTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS, VOL 89, 2019, 89

← 1 2 3 4 5 →