The Rates Of Convergence Of Bayes Estimators In Change-Point Analysis

Abstract

In the asymptotic setting of the change-point estimation problem the limiting behavior of Bayes procedures for the zero-one loss function is studied. The limiting distribution of the difference between the Bayes estimator and the parameter is derived. An explicit formula for the limit of the minimum Bayes risk for the geometric prior distribution is obtained from Spitzer's formula, and the rates of convergence in these limiting relations are determined. Key words and phrases: Bayes risk, change-point problem, convergence rate, geometric distribution, maximum likelihood estimator, Spitzer's formula, zero-one loss function. 1. Asymptotic Behavior of the Bayes Estimator Under Zero-One Loss Function Assume that the observed data is formed by the random subsample (x 0 ; \Delta \Delta \Delta ; x ), which is observed first and is coming from distribution F , and by (x +1 ; \Delta \Delta \Delta ; xn+1 ) from distribution G; G 6= F . In other terms x = (x 0 ; x 1 ; \Delta \Delta \Delta ; x ..