The Asymptotic behavior of the Likelihood Ratio Statistic for Testing a Shift in Mean in a Sequence of Independent Normal Variates.

Abstract

This document considers the problem of testing a sequence of independent and normally distributed random variables with common mean against alternatives involving a shift in the mean at an unknown time point. The purpose of this paper is to study the asymptotic operating characteristics of the likelihood ration test. In the next section, the authors derive, by invoking a result of Darling and Erdos (1956), the asymptotic null distribution of the likelihood ration test, which is related to the extreme value behavior of the Ornstein-Uhlenbeck process. Section 3 studies the asymptotic operating characteristics of the likelihood ratio test and make comparisons between likelihood ration and Bayesian tests.

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