Multivariate Smoothing Regression of Vector Valued Functions with Error in Variables Using a Bayesian Approach

• Activity Number: 369
• Type: Contributed
• Date/Time: Tuesday, August 2, 2016 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Eduardo Trujillo Rivera*
• Keywords: Smoothing Splines ; Error in Variables ; Bayesian ; Vector Valued Function

Abstract

The non-parametric regression is an extremely difficult task in the presence of covariate measurement error. There are various frequentist approaches for this problem which are based on deconvolution or use EM techniques, while there are a few Bayesian methods; all these methods are for the case of a single covariate. In this presentation we describe a Bayesian approach to estimate vector valued regression function which depend on one or more variables when the covariates are measured with error. We take into advantage that the non-error in variable regression problem can be addressed by minimizing a family of functionals and the solution to this minimization problem has a Bayesian interpretation which we incorporate to the error in variable problem. We use Markov Chain Monte Carlo (MCMC) techniques to simulate from the posterior distribution. The use of the MCMC machinery has the advantage over the frequentist approach that we directly obtain credible intervals for all our estimations. Our goal is to provide the results of a study simulation with differentiable regression functions using the methods we propose and compare the loss of fit as the error in variable increase.