An Adaptive-to-Model Test for Parametric Functional Single-Index Model

Lili Xia, Tingyu Lai and Zhongzhan Zhang ()
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Lili Xia: Faculty of Science, Beijing University of Technology, Beijing 100124, China
Tingyu Lai: School of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China
Zhongzhan Zhang: Faculty of Science, Beijing University of Technology, Beijing 100124, China

Mathematics, 2023, vol. 11, issue 8, 1-25

Abstract: Model checking methods based on non-parametric estimation are widely used because of their tractable limiting null distributions and being sensitive to high-frequency oscillation alternative models. However, this kind of test suffers from the curse of dimensionality, resulting in slow convergence, especially for functional data with infinite dimensional features. In this paper, we propose an adaptive-to-model test for a parametric functional single-index model by using the orthogonality of residual and its conditional expectation. The test achieves model adaptation by sufficient dimension reduction which utilizes functional sliced inverse regression. This test procedure can be easily extended to other non-parametric test methods. Under certain conditions, we prove the asymptotic properties of the test statistic under the null hypothesis, fixed alternative hypothesis and local alternative hypothesis. Simulations show that our test has better performance than the method that does not use functional sufficient dimension reduction. An analysis of COVID-19 data verifies our conclusion.

Keywords: functional data; model checking; sufficient dimension reduction; sliced inverse regression; single-index model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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