A Non-Parametric Test for a Change-Point in Linear Profile Data

Keywords

change-point problem, panel data, statistical process control, linear regression

Abstract

We propose a change-point approach for testing the constancy of regression parameters in a linear profile data set (panel data in econometrics). Each sample collected over time in the historical data set consists of several multivariate observations for which a linear regression model is appropriate. The question now is whether all of the profiles follow a linear regression model with the same parameter vector or whether a change occurred in one or more model parameters after a special sample. We use the partial sum operator in several dimensions to test the null hypothesis "H0: no change-point occurred" and propose a non-parametric size ?-test. In Bischoff and Gegg (2010) we compared our proposed method with the likelihood-ratio-test by Mahmoud et al. (2007) in a simulation study. By these simulations we could show that our procedure can, in contrast to the likelihood-ratio-test, even be applied to the non-normal case. In this paper, however, we show how to compute our proposed test statistic step-by-step by considering an artificial data set.

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