Premium
Exact Slopes of Test Statistics for the Multivariate Exponential Family
Author(s) -
Kim GieWhan
Publication year - 1997
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00071
Subject(s) - mathematics , exponential family , statistics , multivariate statistics , exponential function , combinatorics , statistical hypothesis testing , class (philosophy) , exact test , mathematical analysis , artificial intelligence , computer science
The objective of this paper is to investigate exact slopes of test statistics { T n } when the random vectors X 1 , ..., X n are distributed according to an unknown member of an exponential family { P θ ; θ∈Ω. Here Ω is a parameter set. We will be concerned with the hypothesis testing problem of H 0 θ∈Ω 0 vs H 1 : θ∉Ω 0 where Ω 0 is a subset of Ω. It will be shown that for an important class of problems and test statistics the exact slope of { T n } at η in Ω−Ω 0 is determined by the shortest Kullback–Leibler distance from {θ: T n (λ(θ)) = T n (λ(π))} to Ω 0 , λ θ = E θ )( X ).