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Variable selection of varying dispersion student-t regression models

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Abstract

The Student-t regression model is a useful extension of the normal model, which can be used for statistical modeling of data sets involving errors with heavy tails and/or outliers and providesrobust estimation of means and regression coefficients. In this paper, the varying dispersion Student-t regression model is discussed, in which both the mean and the dispersion depend upon explanatory variables. The problem of interest is simultaneously select significant variables both in mean and dispersion model. A unified procedure which can simultaneously select significant variable is given. With appropriate selection of the tuning parameters, the consistency and the oracle property of the regularized estimators are established. Both the simulation study and two real data examples are used to illustrate the proposed methodologies.

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Author information

Authors and Affiliations

  1. School of Science, Nantong University, Nantong, 226007, China

    Weihua Zhao

  2. School of Finance and Statistics, East China Normal University, 200241, Shanghai, China

    Riquan Zhang

  3. Department of Mathematics, Shanxi Datong University, Datong, 037009, China

    Riquan Zhang

Authors
  1. Weihua Zhao
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  2. Riquan Zhang
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Corresponding author

Correspondence to Riquan Zhang.

Additional information

The research was supported in part by the National Natural Science Foundation of China under Grant Nos. 11171112, 11101114, 11201190, the National Statistical Science Research Major Program of China under GrantNo. 2011LZ051, the 111 Project of China under Grant No. B14019, the Doctoral Fund of Ministry of Educationof China under Grant No. 20130076110004, the Natural Science Project of Jiangsu Province EducationDepartment under Grant No. 13KJB110024, the Natural Science Fund of Nantong University under Grant No.13ZY001, and the Research Project of Social Science and Humanity Fund of the Ministry of Education underGrant No. 14YJC910007.

This paper was recommended for publication by Editor SUN Liuquan.

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Zhao, W., Zhang, R. Variable selection of varying dispersion student-t regression models. J Syst Sci Complex 28, 961–977 (2015). https://doi.org/10.1007/s11424-014-2223-9

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  • DOI: https://doi.org/10.1007/s11424-014-2223-9

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