Detailed Statistical Inference – From Multiple Decisions to Confidence Sets – A Non­Bayesian Approach

Abstract

A new approach to detailed statistical inference for the two-decision and multiple decision problem was developed by Chatterjee and Chattopadhyay (1992, 1993). The procedure developed for the multipledecision case is used here to find a solution to, what may be called, the problem of estimation by a ‘confidence set’ when the parameter space is finite. The confidence set problem in which we are required to state a datadependent measure of ‘confidence’ which can be interpreted in terms of betting odds that are ‘optimal’ under repeated experimentation, is considered. A truncated form of utility function is introduced. The case of the truncated form of logarithmic utility function is considered in detail.

AMS {2000} Subject Classification: 62A01, 62F99.