Sample size, parameter rates and contiguity the I.I.D. case
Let defined on the probability space (X, A, Pθ), where is an open subset of , is a nondecreasing sequence of positive integers tending to ∞ as . Let , be a sequence of positive real numbers tending to ∞ as and set . Finally, let be the restrictions of the probability measures , respectively, to the σ-field . Then a necessary and sufficient condition for the sequences to be contiguous is that , provided certain fairly mild conditions are satisfied.