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Variable selection for joint mean and dispersion models of the inverse Gaussian distribution. (English) Zbl 1410.62132
Summary: 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.

MSC:
62J07 Ridge regression; shrinkage estimators (Lasso)
62G20 Asymptotic properties of nonparametric inference
Software:
GLIM
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