Nonparametric tests for semiparametric regression models

Federico Ferraccioli, Laura M. Sangalli and Livio Finos ()
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Federico Ferraccioli: University of Padova
Laura M. Sangalli: Politecnico di Milano
Livio Finos: University of Padova

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2023, vol. 32, issue 3, No 11, 1106-1130

Abstract: Abstract Semiparametric regression models have received considerable attention over the last decades, because of their flexibility and their good finite sample performances. Here we propose an innovative nonparametric test for the linear part of the models, based on random sign-flipping of an appropriate transformation of the residuals, that exploits a spectral decomposition of the residualizing matrix associated with the nonparametric part of the model. The test can be applied to a vast class of extensively used semiparametric regression models with roughness penalties, with nonparametric components defined over one-dimensional, as well as over multi-dimensional domains, including, for instance, models based on univariate or multivariate splines. We prove the good asymptotic properties of the proposed test. Moreover, by means of extensive simulation studies, we show the superiority of the proposed test with respect to current parametric alternatives, demonstrating its excellent control of the Type I error, accompanied by a good power, even in challenging data scenarios, where instead current parametric alternatives fail.

Keywords: Functional data analysis; Smoothing; Roughness penalty; Sign-flip; primary 62G10; secondary 62G05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11749-023-00868-9

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