Contiguity under locally asymptotically normal alternatives
= Contiguity under locally asymptotically normal alternatives
Under <local asymptotic normality>, a fixed $h/\sqrt n$ shift has a <likelihood ratio> limit $\exp(W-v/2)$ with $W\sim N(0,v)$. This is positive with mean one. <Le Cam first lemma> gives <mutual contiguity> of the product laws, so <consistency (statistics)> at the central parameter transfers to these local alternatives.