Tests for a change-point in linear regression

Abstract

This paper considers a problem of detecting a change-point in a linear model.We discuss analytic properties of the likelihood ratio statistic and study its asymptotic behavior.An approximation for the significance level of the test is provided assuming values of the independent variables are effectively random.We also discuss the power and the robustness of the likelihood ratio test. Introduction.The problem of detecting a change-point in a linear regression model has been addressed by many authors.While likelihood ratio statistics to test for parameter changes in a broader sense, have been derived (Quandt (1960), Worsley (1983)) for simple and multiple regression models, mathematical difficulties associated with the sampling distribution of the likelihood ratio statistic have hindered its application in the past.As discussed in Feder (1975a,b) and Quandt (1958Quandt ( , 1960)), a proposed chi-squared approximation for the null distribution of the likelihood ratio statistic is very poor and maximum likelihood estimators are not asymptotically normal.

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