Tests for the linear hypothesis in semi-functional partial linear regression models

Shuzhi Zhu () and Peixin Zhao
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Shuzhi Zhu: Lingnan Normal University
Peixin Zhao: Chongqing Technology and Business University

Metrika: International Journal for Theoretical and Applied Statistics, 2019, vol. 82, issue 2, No 1, 125-148

Abstract: Abstract An empirical likelihood ratio testing method is proposed, in this paper, for semi-functional partial linear regression models. Two empirical likelihood ratio statistics are employed to test the linear hypothesis of parametric components, then we demonstrate that their asymptotic null distributions are standard Chi-square distributions with the degrees of freedom being independent of the nuisance parameters. We also verify the proposed statistics follow non-central Chi-square distributions under the alternative hypothesis, and their powers are derived. Furthermore, we apply the proposed method to test the significance of parametric components. In addition, a F-test statistic is introduced. Simulations are undertaken to demonstrate the proposed methodologies and the simulation results indicate that the proposed testing methods are workable. A real example is applied for illustration.

Keywords: Empirical likelihood ratio test; Functional partial linear model; Linear hypothesis; Functional data; 62G08; 62G20 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s00184-018-0680-1

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