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
收藏
页码：145 / 164
页数：20
相关论文
共 19 条
  • [1] BAHADUR R, 1965, 5TH P BERK S MATH ST, V1, P13
  • [2] RATES OF CONVERGENCE OF ESTIMATES AND TEST STATISTICS
    BAHADUR, RR
    [J]. ANNALS OF MATHEMATICAL STATISTICS, 1967, 38 (02): : 303 - &
  • [3] BAHADUR RR, SOME LIMIT THEOREMS
  • [4] Barndorff-Nielsen O. E., 1978, INFORM EXPONENTIAL F, P111
  • [5] Corless R., 1993, MAPLE TECHNICAL NEWS, V9, P12
  • [6] On the Lambert W function
    Corless, RM
    Gonnet, GH
    Hare, DEG
    Jeffrey, DJ
    Knuth, DE
    [J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 1996, 5 (04) : 329 - 359
  • [7] GAUDOIN O, 1992, IEEE T RELIABILITY, V41
  • [8] Kleinrock L., 1975, QUEUEING SYST, V1, p[71, 119]
  • [9] Lehmann E. L., 1964, TESTING STAT HYPOTHE
  • [10] NIKITIN Y, 1995, ASYMPTOTIC EFFICIENC, P1
12