Robust mean change-point detecting through Laplace linear regression using EM algorithm. (English) Zbl 1442.62158

Summary: 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.


62J05 Linear regression; mixed models
62F03 Parametric hypothesis testing
62F35 Robustness and adaptive procedures (parametric inference)
Full Text: DOI


[1] Chen, J.; Gupta, A. K., Parametric Statistical Change Point Analysis: with Applications to Genetics, Medicine, and Finance (2012), Boston, Mass, USA: Birkhäauser, Boston, Mass, USA · Zbl 1273.62016
[2] Schwarz, G., Estimating the dimension of a model, The Annals of Statistics, 6, 2, 461-464 (1978) · Zbl 0379.62005
[3] Chen, J., Testing for a change point in linear regression models, Communications in Statistics. Theory and Methods, 27, 10, 2481-2493 (1998) · Zbl 0926.62011
[4] Chen, J.; Gupta, A. K., Change point analysis of a Gaussian model, Statistical Papers, 40, 3, 323-333 (1999) · Zbl 0937.62023
[5] Chen, J.; Wang, Y.-P., A statistical change point model approach for the detection of DNA copy number variations in array CGH data, IEEE Transactions on Computational Biology and Bioinformatics, 6, 4, 529-541 (2009)
[6] Osorio, F.; Galea, M., Detection of a change-point in Student-t linear regression models, Statistical Papers, 47, 1, 31-48 (2006) · Zbl 1086.62077
[7] Lin, J. G.; Chen, J.; Li, Y., Bayesian analysis of student t linear regression with unknown change-point and application to stock data analysis, Computational Economics, 40, 3, 203-217 (2012)
[8] Kotz, S.; Kozubowski, T. J.; Podgorski, K., The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering, and Finance (2001), Boston, Mass, USA: Birkhäuser, Boston, Mass, USA · Zbl 0977.62003
[9] Purdom, E.; Holmes, S. P., Error distribution for gene expression data, Statistical Applications in Genetics and Molecular Biology, 4, 1, 1-33 (2005) · Zbl 1083.62114
[10] Pop, M.-I., Distribution of the daily sunspot number variation for the last 14 solar cycles, Solar Physics, 276, 1-2, 351-361 (2012)
[11] Noble, P. L.; Wheatland, M. S., Origin and use of the laplace distribution in daily sunspot numbers, Solar Physics, 282, 2, 565-578 (2013)
[12] van Sanden, S.; Burzykowski, T., Evaluation of Laplace distribution-based ANOVA models applied to microarray data, Journal of Applied Statistics, 38, 5, 937-950 (2011)
[13] Phillips, R. F., Least absolute deviations estimation via the EM algorithm, Statistics and Computing, 12, 3, 281-285 (2002)
[14] Park, T.; Casella, G., The Bayesian lasso, Journal of the American Statistical Association, 103, 482, 681-686 (2008) · Zbl 1330.62292
[15] Song, W.; Yao, W.; Xing, Y., Robust mixture regression model fitting by Laplace distribution, Computational Statistics & Data Analysis, 71, 128-137 (2014) · Zbl 1471.62189
[16] Andrews, D. F.; Mallows, C. L., Scale mixtures of normal distributions, Journal of the Royal Statistical Society B, 36, 1, 99-102 (1974) · Zbl 0282.62017
[17] Barndorff-Nielsen, O. E.; Shephard, N., Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics, Journal of the Royal Statistical Society B Statistical Methodology, 63, 2, 167-241 (2001) · Zbl 0983.60028
[18] Holbert, D., A Bayesian analysis of a switching linear model, Journal of Econometrics, 19, 1, 77-87 (1982)
[19] Vostrikova, L. J., Detecting disorder in multidimensional random processes, Soviet Mathematics Doklady, 24, 1, 55-59 (1981) · Zbl 0487.62072
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.