We propose an iterative algorithm to select the smoothing parameters in additive quantile regression, wherein the functional forms of the covariate effects are unspecified and expressed via B-spline bases with difference penalties on the spline coefficients. The proposed algorithm relies on viewing the penalized coefficients as random effects from the symmetric Laplace distribution, and it turns out to be very efficient and particularly attractive with multiple smooth terms. Through simulations we compare our proposal with some alternative approaches, including the traditional ones based on minimization of the Schwarz Information Criterion. A real-data analysis is presented to illustrate the method in practice.
Bibliographical noteFunding Information:
Data illustrated in Section 5 have been kindly provided by Professor M. Bellafiore, ?Dipartimento di Scienze Psicologiche, Pedagogiche e della Formazione? University of Palermo.We would like to thank the Editor Professor Arno?t Kom?rek, the Associate Editor and the referees for their suggestions and carefully reading of the manuscript which lead to a substantial improvement of the article.
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