Place: Fields Institute (Room 210)
Date: November 18 , 2016 (13:30-15:00)
Speaker: Haosui Duanmu
Title: Nonstandard analysis and its application to statistical decision theory
Abstract: Statistical decision theory has been serving as a rigorous foundation for statistics since its development in the mid 20th century. For statistical decision problem with finite parameter space, every admissible estimator is Bayes which is the well-known complete class theorem. However, such relation begins to break down for general parameter spaces. By using nonstandard analysis, we introduce the notion of hyperfinite statistical decision problem and develop the nonstandard complete class theorem. We show that if there exists a suitable hyperfinite representation of the original statistical decision problem then the nonstandard counterpart of every standard admissible estimator is nonstandard Bayes. We close with a standard complete class theorem for compact parameter spaces.