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Regularized Bayesian quantile regression.


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Adlouni, Salaheddine El; Salaou, Garba; St-Hilaire, André (2018). Regularized Bayesian quantile regression. Communications in Statistics - Simulation and Computation , vol. 47 , nº 1. p. 277-293. DOI: 10.1080/03610918.2017.1280830.

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A number of nonstationary models have been developed to estimate extreme events as function of covariates. A quantile regression (QR) model is a statistical approach intended to estimate and conduct inference about the conditional quantile functions. In this article, we focus on the simultaneous variable selection and parameter estimation through penalized quantile regression. We conducted a comparison of regularized Quantile Regression model with B-Splines in Bayesian framework. Regularization is based on penalty and aims to favor parsimonious model, especially in the case of large dimension space. The prior distributions related to the penalties are detailed. Five penalties (Lasso, Ridge, SCAD0, SCAD1 and SCAD2) are considered with their equivalent expressions in Bayesian framework. The regularized quantile estimates are then compared to the maximum likelihood estimates with respect to the sample size. A Markov Chain Monte Carlo (MCMC) algorithms are developed for each hierarchical model to simulate the conditional posterior distribution of the quantiles. Results indicate that the SCAD0 and Lasso have the best performance for quantile estimation according to Relative Mean Biais (RMB) and the Relative Mean-Error (RME) criteria, especially in the case of heavy distributed errors. A case study of the annual maximum precipitation at Charlo, Eastern Canada, with the Pacific North Atlantic climate index as covariate is presented.

Type de document: Article
Mots-clés libres: asymmetric Laplace distribution; bayesian inference; B-splines; Lasso; quantile regression; Ridge, SCAD
Centre: Centre Eau Terre Environnement
Date de dépôt: 29 janv. 2018 21:29
Dernière modification: 26 mars 2018 13:53
URI: http://espace.inrs.ca/id/eprint/6354

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