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Partial sum process to check regression models with multiple correlated response: With an application for testing a change-point in profile data

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  • Bischoff, W.
  • Gegg, A.

Abstract

We consider regression models with multiple correlated responses for each design point. Under the null hypothesis, a linear regression is assumed. For the least-squares residuals of this linear regression, we establish the limit of the partial sums. This limit is a projection on a certain subspace of the reproducing Kernel Hilbert space of a multivariate Brownian motion. Based on this limit, we propose a significance test of Kolmogorov-Smirnov type to test the null hypothesis and show that this result can be used to study a change-point problem in the case of linear profile data (panel data). We compare our proposed method, which does not rely on any distributional assumptions, with the likelihood ratio test in a simulation study.

Suggested Citation

  • Bischoff, W. & Gegg, A., 2011. "Partial sum process to check regression models with multiple correlated response: With an application for testing a change-point in profile data," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 281-291, February.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:2:p:281-291
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    References listed on IDEAS

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    1. Bischoff, Wolfgang & Somayasa, Wayan, 2009. "The limit of the partial sums process of spatial least squares residuals," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2167-2177, November.
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    Cited by:

    1. Wayan Somayasa & Gusti N. Adhi Wibawa & La Hamimu & La Ode Ngkoimani, 2016. "Asymptotic Theory in Model Diagnostic for General Multivariate Spatial Regression," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-16, September.
    2. Zhuoheng Chen & Yijun Hu, 2017. "Cumulative sum estimator for change-point in panel data," Statistical Papers, Springer, vol. 58(3), pages 707-728, September.

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