Statistical Inference Based on Unbiased Estimators for Intervals of Random Length*

Abstract

An estimator for a distribution quintile is proposed and studied with the use of the unbiased approach within the framework of the exponential distribution family model. The application of the quintile of the distribution function’s unbiased estimator to the construction of a chi-square test for the hypothesis about distribution type is justified. Limit behavior of the Bayes risk estimator for the optimal decision rule of group classification is studied under the assumption that the elements of training samples have distributions belonging to the same one-parameter exponential family.