Revisiting Local Asymptotic Normality (LAN) and Passing on to Local Asymptotic Mixed Normality (LAMN) and Local Asymptotic Quadratic (LAQ) Experiments

Abstract

Let X 1, …, X n be a random sample of size n from an underlying parametric statistical model. Then the basic statistical problem may be stated as follows: On the basis of a random sample, whose probability law depends on a parameter θ, discriminate between two values θ and θ ∗ (θ≠θ∗). When the parameters are sufficiently far apart, any decent statistical procedure will do the job. A problem arises when the parameter points are close together, and yet the corresponding probability measures are substantially or even vastly different. The present paper revolves around ways of resolving such a problem. The concepts and methodology used are those of contiguity, Local Asymptotic Normality (LAN), Local Asymptotic Mixed Normality (LAMN), and Local Asymptotic Quadratic (LAQ) experiments.