Cornell Math - MATH 674, Spring 2000

MATH 674 — Spring 2000
Introduction to Mathematical Statistics

The notion of statistical experiment will be at the center of the course. An experiment is an indexed family of probability measures; statistical decisions about the index (parameter) are evaluated by their risk functions. The Le Cam delta distance between experiments serves to compare these objects with regard to their informational content. Equivalence classes are introduced and characterized in terms of sufficient statistics and likelihood processes. A final goal is to establish various analogs of the central limit theorem, allowing reduction of general decision problems to those in Gaussian experiments.

The course will initially focus on the binary case, where there are just two probability measures (hypotheses) which have to be distinguished. Topics in stochastic processes and functional analysis will be touched upon as the need arises. A main reference is

Strasser, H., Mathematical Theory of Statistics. Walter de Gruyter, Berlin, 1985.

but typed handouts will be presented thoughout the course, making it self-contained.