Change-point Estimation via Empirical Likelihood for a Segmented Linear Regression

by Zhihua Liu and Lianfen Qian.

Abstract: For a segmented regression system with an unknown change-point over two domains of a predictor, a new empirical likelihood ratio statistic is proposed to test the null hypothesis of no change. Under the null hypothesis of no change, the proposed test statistic is empirically shown asymptotically Gumbel distributed with robust location and scale parameters against various parameter settings and error distributions. Under the alternative hypothesis with a change-point, the test statistic is utilized to estimate the change point between the two domains. The power analysis shows that the proposed test is tractable. An empirical example on analyzing the plasma osmolality data is given.

Key Words: Empirical likelihood ratio, Gumbel extreme value distribution, segmented linear regression, change-point

Authors:
Zhihua Liu, amoyparsa@gmail.com
Lianfen Qian, lqian@fau.edu

Editor: Suojin Wang, sjwang@PICARD.tamu.edu

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