Variable selection of varying dispersion student-t regression models

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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