Test and Estimation for a Change-point in the Linear Structural Error-in-Variables Models

In this paper, we discuss the hypothesis tests and estimation for most one change-point in the linear structural error-in-variables model. Firstly, we propose likelihood ratio test statistic by using maximum likelihood ratio method. Applying Schwarz information criterion, we respectively derive the corresponding test statistics in terms of the principle of minimum information criterion, as redundant parameters are known and unknown. The asymptotic problem is considered with test statistic in the case of redundant parameters unknown. By a simple calculation, we conclude that the maximum likelihood estimation of change-point and the estimation of change-point under Schwarz information criterion are the same. We also obtain the limiting distribution of the estimation of change-point. Some Monte-Carlo simulation studies are given under each null hypothesis.