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On the effect of overdispersion on exact conditional tests

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Let Y1, . . ., Yn denote independent random variables such that Yj has a one-parameter exponential family distribution with canonical parameter θj=λ+ψXj; here X1, . . ., Xn are known constants. Consider a test of the null hypothesis ψ=0. Under the null hypothesis, AYj is sufficient for λ and, hence, a test of ψ=0 may be based on the conditional distribution of TXjYj given A, which is independent of λ. In this paper, the effects of overdispersion due to a mixture model on the conditional distribution of T given A are considered.
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Keywords: Asymptotic expansions; Conditional inference; Exact tests; Mixture models; Robustness; Significance tests

Document Type: Original Article

Affiliations: Northwestern University, Evanston, USA

Publication date: 1999-01-01

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