On the effect of overdispersion on exact conditional tests
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, A=ΣYj is sufficient for λ and, hence, a test of ψ=0 may be based on the conditional distribution of T=ΣXjYj 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.