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Bayes variable selection in semiparametric linear models.

Suprateek Kundu1, David B Dunson2

  • 1Postdoctoral Research Associate in the Dept. of Statistics, Texas A&M University, College Station, TX 77843, USA.

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|July 30, 2014
PubMed
Summary
This summary is machine-generated.

This study extends Bayesian variable selection methods for parametric models to semiparametric linear regression. It introduces a novel semiparametric g-prior for models with unknown residual densities, ensuring variable selection consistency.

Keywords:
Asymptotic theoryBayes factorLarge pModel selectionPosterior consistencyStochastic search variable selectionSubset selectiong-priorsmall n

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Area of Science:

  • Statistics
  • Machine Learning
  • Econometrics

Background:

  • Established Bayesian variable selection methods primarily focus on parametric models.
  • Generalizing these techniques to semiparametric models with unknown residual densities presents a significant challenge.

Purpose of the Study:

  • To extend existing Bayesian variable selection methods and asymptotic theory for g-priors to semiparametric linear regression.
  • To develop a novel semiparametric g-prior suitable for models with unknown residual densities.

Main Methods:

  • Utilized a Dirichlet process location mixture for modeling unknown residual densities.
  • Proposed a semiparametric g-prior incorporating cluster allocation indicators.
  • Employed a stochastic search variable selection algorithm for posterior computation.

Main Results:

  • Demonstrated the feasibility of posterior computation using the proposed algorithm.
  • Established Bayes factor and variable selection consistency under specific prior conditions.
  • Showed consistency even when the number of predictors (p) grows faster than the sample size (n).

Conclusions:

  • The proposed semiparametric g-prior offers a robust approach for variable selection in linear regression with unknown residual densities.
  • The method maintains desirable asymptotic properties, including consistency, under challenging conditions of high dimensionality.