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Bayesian P-Splines Applied to Semiparametric Models with Errors Following a Scale Mixture of Normals

Author

Listed:
  • Marcelo M. Taddeo

    (Federal University of Bahia)

  • Pedro A. Morettin

    (University of São Paulo)

Abstract

This work is about semiparametric models assuming that the error follows a scale mixture of gaussian distributions and such that the functional relation between the response and explanatory variables is unknown. This class of distributions is particularly interesting since it includes heavy tailed distributions such as the Student’s t, symmetric stable distributions and double exponential. They are specially useful for modelling data with high incidence of extreme values. Exploring the nature of these distributions and using the concept of P-splines we obtain the complete posterior conditional distributions of all the parameters involved in the model and apply the Gibbs sampler. In this way, we show how to combine P-splines and mixture of normals under a Bayesian perspective in order to estimate such curves. We conduct some simulations in order to illustrate the proposed methodology and also analyze the case of partially linear models.

Suggested Citation

  • Marcelo M. Taddeo & Pedro A. Morettin, 2023. "Bayesian P-Splines Applied to Semiparametric Models with Errors Following a Scale Mixture of Normals," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1331-1355, August.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:2:d:10.1007_s13171-022-00290-7
    DOI: 10.1007/s13171-022-00290-7
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    References listed on IDEAS

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    1. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    2. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    3. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    4. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    5. Porto, Rogério F. & Morettin, Pedro A. & Aubin, Elisete C.Q., 2008. "Wavelet regression with correlated errors on a piecewise Hölder class," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2739-2743, November.
    6. Holland, Ashley D., 2017. "Penalized spline estimation in the partially linear model," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 211-235.
    7. Iain M. Johnstone & Bernard W. Silverman, 1997. "Wavelet Threshold Estimators for Data with Correlated Noise," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 319-351.
    8. Golubev, Georgi & Härdle, Wolfgang, 2000. "On adaptive estimation in partial linear models," SFB 373 Discussion Papers 2000,21, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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