Bayes variable selection in semiparametric linear models

• Autores: Suprateek Kundu, David B. Dunson
• Localización: Journal of the American Statistical Association, ISSN 0162-1459, Vol. 109, Nº 505, 2014, págs. 437-447
• Idioma: inglés
• DOI: 10.1080/01621459.2014.881153
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• Resumen

  • There is a rich literature on Bayesian variable selection for parametric models. Our focus is on generalizing methods and asymptotic theory established for mixtures of g-priors to semiparametric linear regression models having unknown residual densities. Using a Dirichlet process location mixture for the residual density, we propose a semiparametric g-prior which incorporates an unknown matrix of cluster allocation indicators. For this class of priors, posterior computation can proceed via a straightforward stochastic search variable selection algorithm. In addition, Bayes� factor and variable selection consistency is shown to result under a class of proper priors on g even when the number of candidate predictors p is allowed to increase much faster than sample size n, while making sparsity assumptions on the true model size.