Synopses & Reviews
This Tract presents an elaboration of the notion of 'contiguity', which is a concept of 'nearness' of sequences of probability measures. It provides a powerful mathematical tool for establishing certain theoretical results with applications in statistics, particularly in large sample theory problems, where it simplifies derivations and points the way to important results. The potential of this concept has so far only been touched upon in the existing literature, and this book provides the first systematic discussion of it. Alternative characterizations of contiguity are first described and related to more familiar mathematical ideas of a similar nature. A number of general theorems are formulated and proved. These results, which provide the means of obtaining asymptotic expansions and distributions of likelihood functions, are essential to the applications which follow.
Table of Contents
1. On the concept of contiguity and related theorems; 2. Asymptotic expansion and asymptotic distribution of likelihood functions; 3. Approximation of a given family of probability measures by an exponential family - asymptotic sufficiency; 4. Some statistical applications: AUMP and AUMPU tests for certain testing hypotheses problems; 5. Some statistical applications: asymptotic efficiency of estimates; 6. Multiparameter asymptotically optimal tests.