Confidence Distributions for Skew Normal Change Point Model Based on Modified Information Criterion

In this paper, we consider a skew normal change-point model. Instead of only providing the point estimate of the change location, we propose an estimating procedure based on the confidence distribution combining with the modified information criterion to construct the confidence set for the change location. The simulations indicate the advantages of the proposed method comparing to the existing method in terms of coverage probabilities and average lengths of the confidence sets, especially when the change occurs at the very beginning or in the very end. The proposed method is applied to two stock market data to illustrate the detection and the estimation procedures.