Title: Bayesian approach to smoothing parameter selection in spline estimate for regression curve

Authors: Sonia Amroun; Lamia Djerroud; Smail Adjabi

Addresses: Research Unit LaMOS, University of Bejaia, Algeria ' Research Unit LaMOS, University of Bejaia, Algeria ' Research Unit LaMOS, University of Bejaia, Algeria

Abstract: Spline functions have proved to be very useful in statistics, in particular, to estimate the nonparametric regression. Many different smoothing parameter selectors for the smoothing spline are proposed in the literature such as cross-validation (CV), generalised cross-validation (GCV). In this article, we propose the Bayesian approach to estimate the smoothing parameter and the variance of the Gaussian error model in the context of the nonparametric regression. We use the Markov chain Monte Carlo (MCMC) method to compute the estimators given by the proposed Bayesian approach. The performance of the Bayesian approach is compared with the classical generalised cross-validation method through simulation and real data.

Keywords: nonparametric regression; smoothing spline; Bayesian approach; smoothing parameter.

DOI: 10.1504/IJCSM.2020.111702

International Journal of Computing Science and Mathematics, 2020 Vol.12 No.3, pp.216 - 227

Received: 03 Jan 2018
Accepted: 21 May 2018
Published online: 11 Dec 2020 *

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