Cusum Test for Parameter Change Based on the Maximum Likelihood Estimator

Sangyeol Lee · Taewook Lee

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Advanced Statistical Process Monitoring Probability and Statistical Research Statistical Methods and Inference

Abstract

In this paper we consider the problem of testing for a parameter change based on the cusum test (cf. Lee, S.; Ha, J.; Na, O.; Na, S. The cusum test for parameter change in time series models. Scand. J. Statist. 2003, 30, 651–739) utilizing the maximum likelihood estimator. The issue is handled in iid random samples, and then special attention is paid to hidden Markov models. It is shown that the limiting distribution of the cusum test statistic is the sup of a standard Brownian bridge under regularity conditions. A simulation result is provided for illustration.

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1994Use of Cumulative Sums of Squares for Retrospective Detection of Changes of Variance 1997Limit theorems in change-point analysis 1955A Test for a Change in a Parameter Occurring at an Unknown Point 2011Parametric Statistical Change Point Analysis 1994Use of Cumulative Sums of Squares for Retrospective Detection of Changes of Variance 2000Parametric Statistical Change Point Analysis 2003The Cusum Test for Parameter Change in Time Series Models 1996On the Rate of Approximations for Maximum Likelihood Tests in Change-Point Models

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