Contiguity of measures

Summary

Contiguity is an asymptotic form of absolute continuity for sequences of probability measures. A sequence $(Q_n)$ is contiguous with respect to $(P_n)$ if every sequence of events whose $P_n$-probability tends to zero also has $Q_n$-probability tending to zero. It was introduced by Lucien Le Cam. It lets one transfer convergence in probability from a null hypothesis to nearby alternatives. This is the basis of asymptotic power calculations and of local asymptotic theory.