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Bayesian inference for semiparametric regression using a Fourier representation

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  • P. J. Lenk

Abstract

This paper presents the Bayesian analysis of a semiparametric regression model that consists of parametric and nonparametric components. The nonparametric component is represented with a Fourier series where the Fourier coefficients are assumed a priori to have zero means and to decay to 0 in probability at either algebraic or geometric rates. The rate of decay controls the smoothness of the response function. The posterior analysis automatically selects the amount of smoothing that is coherent with the model and data. Posterior probabilities of the parametric and semiparametric models provide a method for testing the parametric model against a non‐specific alternative. The Bayes estimator’s mean integrated squared error compares favourably with the theoretically optimal estimator for kernel regression.

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  • 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.
    • Handle: RePEc:bla:jorssb:v:61:y:1999:i:4:p:863-879
    DOI: 10.1111/1467-9868.00207
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    Cited by:

    1. Hongchang Hu & Yu Zhang & Xiong Pan, 2016. "Asymptotic normality of DHD estimators in a partially linear model," Statistical Papers, Springer, vol. 57(3), pages 567-587, September.
    2. Jean-Yves Dauxois & Pierre Druilhet & Denys Pommeret, 2006. "A bayesian choice between poisson, binomial and negative binomial models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 423-432, September.
    3. 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.
    4. Garnett P. McMillan & Timothy E. Hanson & Gabrielle Saunders & Frederick J. Gallun, 2013. "A two-component circular regression model for repeated measures auditory localization data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(4), pages 515-534, August.
    5. 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.
    6. Lee, Jaeyong & Oh, Hee-Seok, 2013. "Bayesian regression based on principal components for high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 175-192.
    7. Timothy J. Gilbride & Peter J. Lenk & Jeff D. Brazell, 2008. "Market Share Constraints and the Loss Function in Choice-Based Conjoint Analysis," Marketing Science, INFORMS, vol. 27(6), pages 995-1011, 11-12.
    8. Paciorek, Christopher J., 2007. "Computational techniques for spatial logistic regression with large data sets," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3631-3653, May.

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