Abstract
We proposed a robust mean change-point estimation algorithm in linear regression with the assumption that the errors follow the Laplace distribution. By representing the Laplace distribution as an appropriate scale mixture of normal distribution, we developed the expectation maximization (EM) algorithm to estimate the position of mean change-point. We investigated the performance of the algorithm through different simulations, finding that our methods is robust to the distributions of errors and is effective to estimate the position of mean change-point. Finally, we applied our method to the classical Holbert data and detected a change-point.
Highlights
Change-point analysis has been an active research area since the early 1950s
By representing the Laplace distribution as an appropriate scale mixture of normal distribution, we developed the expectation maximization (EM) algorithm to estimate the position of mean change-point
We study the single mean change-point problem in linear regression model assuming that the error follows the Laplace distribution via EM algorithm and use the Schwarz information criterion (SIC) model selection method to estimate the position of the mean change-point
Summary
Change-point analysis has been an active research area since the early 1950s. During the following period of sixty-some years, numerous articles have been published in various journals and proceedings. Chen and Wang [5] developed a statistical change-point model approach for the detection of DNA copy number variations in array CGH data using the SIC method and assuming the error follows the normal distribution. The normal assumption is not always suitable, for a lot of real data usually shows heavy tail and skewness In such cases, some robust change-point detecting model with heavy-tailed distribution might be better than the normal model. Song et al [15] proposed a robust estimation procedure for mixture linear regression models assuming that the error terms follow the Laplace distribution. We study the single mean change-point problem in linear regression model assuming that the error follows the Laplace distribution via EM algorithm and use the SIC model selection method to estimate the position of the mean change-point. We apply our method to some stock market data set
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