Testing and Interval Estimation in a Change-Point Model Allowing at Most One Change

摘要

This paper considers the simplest model of change-point in which at most one change in the mean may occur. Results include: 1) Introduction of a test for the null hypothesis that no change in the mean occurs, and the limit distribution of the test-statistic; 2) Approximate calculation of the power of the test; 3) Interval estimation of the position of change; 4) Point estimation of the jump at the point of change and its asymptotic distribution; and 5) Evaluation of the bias of the MLE of error variance.