Dec. 19 2006 2:00PM

Dec. 19 2006 3:00PM

In this lecture we consider the standard model (X, A, P) of mathematical statistics, where P is a class of mutually equivalent probability measures on (X, A). The important particular problem of testing statistical hypotheses will be discussed. Independent observations X1,...,X2 from the sample space (X, A, Po) will be considered. We will interested in application of the f-divergences Df(Po, P) in this problem.

Various methods of bypassing the difficulties of proposed problem will be mentioned. They lead to classes of minimum distance tests. Most of them were based on discretizations of the statistical model using finite deterministic or random quantizations of the observation space X. Our proposal is different, we replace Df(Pn, P) by supremum Df(Pn, P|Q). The main result is that the general maximum likelikood statistics are special cases for f(t) = t ln(t). The details will be introduced in the lecture.

Pravidelný seminář Rozhodování a řízení za neurčitosti. (Contact person: Miroslav Kárný)