Robustness of the Likelihood Ratio Test for a Change in Simple Linear Regression
研究了简单线性回归中变化点似然比检验在非正态分布下的稳健性，通过理论证明和模拟验证了检验统计量的分布不敏感性，对使用回归分析的经济学者判断检验可靠性有帮助。
Abstract This article examines the robustness of the likelihood ratio tests for a change point in simple linear regression. We first summarize the normal theory of Kim and Siegmund, who have considered the likelihood ratio tests for no change in the regression coefficients versus the alternatives with a change in the intercept alone and with a change in the intercept and slope. We then discuss the robustness of these tests. Using the convergence theory of stochastic processes, we show that the test statistics converge to the same limiting distributions regardless of the underlying distribution. We perform simulations to assess the distributional insensitivity of the test statistics to a Weibull, a lognormal, and a contaminated normal distribution in two different cases: fixed and random independent variables. Numerical examples illustrate that the test has a correct size and retains its power when the distribution is nonnormal. We also study the effects of the independent variable's configuration with the aid of a numerical example. Key Words: Asymptotic tail distributionDistributional insensitivityPowerSignificance levelTwo-phase regression