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A semiparametric scale-mixture regression model and predictive recursion maximum likelihood

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  • Martin, Ryan
  • Han, Zhen

Abstract

To avoid specification of a particular distribution for the error in a regression model, we propose a flexible scale mixture model with a nonparametric mixing distribution. This model contains, among other things, the familiar normal and Student-t models as special cases. For fitting such mixtures, the predictive recursion method is a simple and computationally efficient alternative to existing methods. We define a predictive recursion-based marginal likelihood function, and estimation of the regression parameters proceeds by maximizing this function. A hybrid predictive recursion–EM algorithm is proposed for this purpose. The method’s performance is compared with that of existing methods in simulations and real data analyses.

Suggested Citation

  • Martin, Ryan & Han, Zhen, 2016. "A semiparametric scale-mixture regression model and predictive recursion maximum likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 75-85.
    • Handle: RePEc:eee:csdana:v:94:y:2016:i:c:p:75-85
    DOI: 10.1016/j.csda.2015.08.005
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    References listed on IDEAS

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    1. Barros, Michelli & Paula, Gilberto A. & Leiva, Víctor, 2009. "An R implementation for generalized Birnbaum-Saunders distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1511-1528, February.
    2. Gilberto A. Paula & Víctor Leiva & Michelli Barros & Shuangzhe Liu, 2012. "Robust statistical modeling using the Birnbaum‐Saunders‐t distribution applied to insurance," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 28(1), pages 16-34, January.
    3. Hinkley, D. V., 1997. "Discussion of paper by H. Li & G.S. Maddala," Journal of Econometrics, Elsevier, vol. 80(2), pages 319-323, October.
    4. Koller, Manuel & Stahel, Werner A., 2011. "Sharpening Wald-type inference in robust regression for small samples," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2504-2515, August.
    5. Ryan Martin & Surya T. Tokdar, 2011. "Semiparametric inference in mixture models with predictive recursion marginal likelihood," Biometrika, Biometrika Trust, vol. 98(3), pages 567-582.
    6. Jara, Alejandro & Hanson, Timothy & Quintana, Fernando A. & Müller, Peter & Rosner, Gary L., 2011. "DPpackage: Bayesian Semi- and Nonparametric Modeling in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i05).
    7. Yong Wang, 2007. "On fast computation of the non‐parametric maximum likelihood estimate of a mixing distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 185-198, April.
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    Cited by:

    1. Vaidehi Dixit & Ryan Martin, 2022. "Estimating a Mixing Distribution on the Sphere Using Predictive Recursion," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 596-626, November.
    2. Ryan Martin, 2021. "A Survey of Nonparametric Mixing Density Estimation via the Predictive Recursion Algorithm," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 97-121, May.
    3. Chee, Chew-Seng & Seo, Byungtae, 2020. "Semiparametric estimation for linear regression with symmetric errors," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).

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