Statistical Modelling 21 (5) (2021), 428–448

Multiple smoothing parameters selection in additive regression quantiles

Vito M.R. Muggeo,
Dipartimento di Scienze Economiche,
Aziendali e Statistiche,
University of Palermo,
Palermo,
Italy.
e-mail: vito.muggeo@unipa.it

Federico Torretta,
Dipartimento di Scienze Economiche,
Aziendali e Statistiche,
University of Palermo,
Palermo,
Italy.

Paul H. C. Eilers,
Erasmus University Medical Centre,
Rotterdam,
The Netherlands.

Mariangela Sciandra,
Dipartimento di Scienze Economiche,
Aziendali e Statistiche,
University of Palermo,
Palermo,
Italy.

Massimo Attanasio,
Dipartimento di Scienze Economiche,
Aziendali e Statistiche,
University of Palermo,
Palermo,
Italy.

Abstract:

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.

Keywords:

additive quantile regression, P-splines, Schall algorithm, flexible modelling, semiparametric quantile regression

Downloads:

Example data and code in zipped archive; Supplementary material (PDF)
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