On the effect of overdispersion on exact conditional tests
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1999 · Volume 61 · Issue 1
Abstract
LetY1, . . .,Yndenote independent random variables such thatYjhas a one-parameter exponential family distribution with canonical parameter θj=λ+ψXj; hereX1, . . .,Xnare known constants. Consider a test of the null hypothesis ψ=0. Under the null hypothesis,A=ΣYjis sufficient for λ and, hence, a test of ψ=0 may be based on the conditional distribution ofT=ΣXjYjgivenA, which is independent of λ. In this paper, the effects of overdispersion due to a mixture model on the conditional distribution ofTgivenAare considered.
Keywords
Asymptotic expansions, Conditional inference, Exact tests, Mixture models, Robustness, Significance tests
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