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A note on the Bayes factor in a semiparametric regression model

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  • Choi, Taeryon
  • Lee, Jaeyong
  • Roy, Anindya

Abstract

In this paper, we consider a semiparametric regression model where the unknown regression function is the sum of parametric and nonparametric parts. The parametric part is a finite-dimensional multiple regression function whereas the nonparametric part is represented by an infinite series of orthogonal basis. In this model, we investigate the large sample property of the Bayes factor for testing the parametric null model against the semiparametric alternative model. Under some conditions on the prior and design matrix, we identify the analytic form of the Bayes factor and show that the Bayes factor is consistent, i.e.converges to infinity in probability under the parametric null model, while converges to zero under the semiparametric alternative, as the sample size increases.

Suggested Citation

  • Choi, Taeryon & Lee, Jaeyong & Roy, Anindya, 2009. "A note on the Bayes factor in a semiparametric regression model," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1316-1327, July.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:6:p:1316-1327
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    References listed on IDEAS

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    1. P. J. Lenk, 1999. "Bayesian inference for semiparametric regression using a Fourier representation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 863-879.
    2. R. L. Eubank, 2000. "Testing for No Effect by Cosine Series Methods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 747-763, December.
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    1. repec:dau:papers:123456789/13438 is not listed on IDEAS
    2. Seongil Jo & Taeyoung Roh & Taeryon Choi, 2016. "Bayesian spectral analysis models for quantile regression with Dirichlet process mixtures," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 177-206, March.
    3. He, Heping & Severini, Thomas A., 2016. "A flexible approach to inference in semiparametric regression models with correlated errors using Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 316-329.

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