Two-phase regression with nonhomogeneous errors

Likelihood ratio tests for a change in simple linear regression with unequal variances are studied. We first derive the likelihood ratio statistics assuming nonhomogeneous error variance. (We call such statistics the weighted likelihood ratio statistics.) We obtain analytic approximations for the p-values of these weighted tests, and assess the accuracy of the approximations via simulation. Using numerical examples, we also study the robustness to heteroscedasticity of the unweighted likelihood ratio tests considered in Kim and Siegmund (1989).