Constructing unbiased tests for homogeneity and goodness of fit

Arthur Cohen; H. B. Sackrowitz

doi:https://doi.org/10.1016/0167-7152(91)90106-2

Constructing unbiased tests for homogeneity and goodness of fit

Arthur Cohen, H. B. Sackrowitz

School of Arts and Sciences, Statistics

Rutgers, The State University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Suppose X_ij, i=1, 2,..., k, j=1, 2,..., n_i, are random samples from independent populations distributed according to an exponential family with parameter θ_i. Let Y_i be the minimal sufficient statistic for population i and assume that the sum of any subset of the Y_i, i=1, 2,..., k, is also a one parameter exponential family. The normal and Poisson distributions satisfy such an assumption. The problem is to test H: θ₁=θ₂= ⋯ =θ_k vs K: not H. Unbiased tests are constructed. The construction ca so that the resulting unbiased tests are in a complete class in the continuous case and are admissible in the discrete case. The construction is also appropriate for testing a simple hypothesis concerned with multinomial probabilities against an arbitrary alternative. This latter problem arises in testing goodness of fit.

Original language	American English
Pages (from-to)	351-355
Number of pages	5
Journal	Statistics and Probability Letters
Volume	12
Issue number	4
DOIs	https://doi.org/10.1016/0167-7152(91)90106-2
State	Published - Oct 1991

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Neyman structure
Unbiased test
exponential family
goodness of fit
homogeneity

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https://doi.org/10.1016/0167-7152(91)90106-2

Cite this

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title = "Constructing unbiased tests for homogeneity and goodness of fit",

abstract = "Suppose Xij, i=1, 2,..., k, j=1, 2,..., ni, are random samples from independent populations distributed according to an exponential family with parameter θi. Let Yi be the minimal sufficient statistic for population i and assume that the sum of any subset of the Yi, i=1, 2,..., k, is also a one parameter exponential family. The normal and Poisson distributions satisfy such an assumption. The problem is to test H: θ1=θ2= ⋯ =θk vs K: not H. Unbiased tests are constructed. The construction ca so that the resulting unbiased tests are in a complete class in the continuous case and are admissible in the discrete case. The construction is also appropriate for testing a simple hypothesis concerned with multinomial probabilities against an arbitrary alternative. This latter problem arises in testing goodness of fit.",

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author = "Arthur Cohen and Sackrowitz, {H. B.}",

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TY - JOUR

T1 - Constructing unbiased tests for homogeneity and goodness of fit

AU - Cohen, Arthur

AU - Sackrowitz, H. B.

N1 - Funding Information: by NSF Grant

PY - 1991/10

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N2 - Suppose Xij, i=1, 2,..., k, j=1, 2,..., ni, are random samples from independent populations distributed according to an exponential family with parameter θi. Let Yi be the minimal sufficient statistic for population i and assume that the sum of any subset of the Yi, i=1, 2,..., k, is also a one parameter exponential family. The normal and Poisson distributions satisfy such an assumption. The problem is to test H: θ1=θ2= ⋯ =θk vs K: not H. Unbiased tests are constructed. The construction ca so that the resulting unbiased tests are in a complete class in the continuous case and are admissible in the discrete case. The construction is also appropriate for testing a simple hypothesis concerned with multinomial probabilities against an arbitrary alternative. This latter problem arises in testing goodness of fit.

AB - Suppose Xij, i=1, 2,..., k, j=1, 2,..., ni, are random samples from independent populations distributed according to an exponential family with parameter θi. Let Yi be the minimal sufficient statistic for population i and assume that the sum of any subset of the Yi, i=1, 2,..., k, is also a one parameter exponential family. The normal and Poisson distributions satisfy such an assumption. The problem is to test H: θ1=θ2= ⋯ =θk vs K: not H. Unbiased tests are constructed. The construction ca so that the resulting unbiased tests are in a complete class in the continuous case and are admissible in the discrete case. The construction is also appropriate for testing a simple hypothesis concerned with multinomial probabilities against an arbitrary alternative. This latter problem arises in testing goodness of fit.

KW - Neyman structure

KW - Unbiased test

KW - exponential family

KW - goodness of fit

KW - homogeneity

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JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

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ER -

Constructing unbiased tests for homogeneity and goodness of fit

Abstract

ASJC Scopus subject areas

Keywords

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