A new RKHS-based global testing for functional linear model

Jianjun Xu and Wenquan Cui

Statistics & Probability Letters, 2022, vol. 182, issue C

Abstract: This article studies global testing of the slope function in the functional linear regression model in the framework of reproducing kernel Hilbert space. We propose a new testing statistic based on smoothness regularization estimators. The asymptotic distribution of the testing statistic is established under the null hypothesis. It is shown that the null asymptotic distribution is determined jointly by the reproducing kernel and the covariance function of the covariate. Our theoretical analysis shows that the proposed testing is consistent over a class of smooth local alternatives. Despite the generality of the method of regularization, we show the procedure is easily implementable. Numerical examples are provided to demonstrate the empirical advantages over the competing methods.

Keywords: RKHS; Mercer theorem; Operator; Gaussian process (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2021.109277

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