Statistics and Its Interface

Volume 9 (2016)

Number 1

Detecting change point in linear regression using jackknife empirical likelihood

Pages: 113 – 122

DOI: http://dx.doi.org/10.4310/SII.2016.v9.n1.a11

Authors

Xinqi Wu (School of Mathematical Sciences, University of the Chinese Academy of Sciences, Beijing, China; and Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing, China)

Sanguo Zhang (School of Mathematical Sciences, University of the Chinese Academy of Sciences, Beijing, China; and Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing, China)

Qingzhao Zhang (School of Mathematical Sciences, University of the Chinese Academy of Sciences, Beijing, China; and Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing, China)

Shuangge Ma (Department of Biostatistics, Yale University, New Haven, Connecticut, U.S.A.)

Abstract

Data generated in quite a few examples can be described using a linear regression model with a change point. In this paper for such a model, we develop a nonparametric method based on the jackknife empirical likelihood (JEL) to detect the change in regression coefficients. Under mild conditions, we show that the null distribution of the JEL ratio test statistic is asymptotically Gumbel. The test and the estimator of change point are shown to be consistent under the alternative hypothesis. Simulation suggests that the proposed method is computationally much more affordable than the alternative based on empirical likelihood. We also demonstrate the proposed method using two real datasets.

Keywords

change point, jackknife empirical likelihood, jackknife pseudo-values

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