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Variable selection for joint mean and dispersion models of the inverse Gaussian distribution

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  • Liucang Wu

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  • Huiqiong Li

Abstract

The choice of distribution is often made on the basis of how well the data appear to be fitted by the distribution. The inverse Gaussian distribution is one of the basic models for describing positively skewed data which arise in a variety of applications. In this paper, the problem of interest is simultaneously parameter estimation and variable selection for joint mean and dispersion models of the inverse Gaussian distribution. We propose a unified procedure which can simultaneously select significant variables in mean and dispersion model. With appropriate selection of the tuning parameters, we establish the consistency of this procedure and the oracle property of the regularized estimators. Simulation studies and a real example are used to illustrate the proposed methodologies. Copyright Springer-Verlag 2012

Suggested Citation

  • Liucang Wu & Huiqiong Li, 2012. "Variable selection for joint mean and dispersion models of the inverse Gaussian distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(6), pages 795-808, August.
  • Handle: RePEc:spr:metrik:v:75:y:2012:i:6:p:795-808 DOI: 10.1007/s00184-011-0352-x
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    References listed on IDEAS

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    1. Jin-Guan Lin & Bo-Cheng Wei & Nan-Song Zhang, 2004. "Varying Dispersion Diagnostics for Inverse Gaussian Regression Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(10), pages 1157-1170.
    2. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    3. Harvey, A C, 1976. "Estimating Regression Models with Multiplicative Heteroscedasticity," Econometrica, Econometric Society, vol. 44(3), pages 461-465, May.
    4. A. Antoniadis, 1997. "Wavelets in statistics: A review," Statistical Methods & Applications, Springer;Società Italiana di Statistica, pages 97-130.
    5. Zhao, Peixin & Xue, Liugen, 2010. "Variable selection for semiparametric varying coefficient partially linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1872-1883, September.
    6. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
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    Cited by:

    1. Xu, Dengke & Zhang, Zhongzhan, 2013. "A semiparametric Bayesian approach to joint mean and variance models," Statistics & Probability Letters, Elsevier, pages 1624-1631.

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