On the Estimation of the Order of Smoothness of the Regression Function

• Activity Number: 263
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Daniel Taylor Rodriguez* and Sujit Ghosh
• Companies: SAMSI/Duke University and SAMSI/North Carolina State University
• Keywords: semiparametric regression ; Bernstein polynomials ; order of smoothness ; mixtures of g-priors ; model hierarchical priors

Abstract

The order of smoothness chosen in semiparametric estimation problems is critical. This choice balances the tradeoff between model generality and data overfitting. The most common approach used in this context is cross-validation. However, cross-validation is computationally costly and precludes valid post-selection inference without further considerations. With this in mind, borrowing elements from the Bayesian variable selection literature, we propose an approach to estimate and conduct inference on the order of smoothness for the estimated regression function and the model parameters. Although the method can be extended to most series-based smoothing methods, we focus on estimates arising from Bernstein polynomials for the regression function, using mixtures of g-priors on the model parameter space and a hierarchical specification for the priors on the order of smoothness. The performance of the methods proposed is assessed through simulation experiments.