Tuning Parameter Selector For The Penalized Likelihood Method In Multivariate Generalized Linear Models

Generalized linear models (GLMs), which can model a large variety of data, have a wide area of application. The class of GLMs includes, as special case, linear models, analysis-of-variance models, logistic models for binary data in the form of proportions and many others. Variable selection is fundamental to high dimensional multivariate generalized lin-ear models. The smoothly clipped absolute deviation (SCAD) method proposed by Fan and Li (2001) can·solve the problem of variable selection and estimation in generalized linear models with canonical link functions. The choice of the tuning parameter in the SCAD method is critical, which controls the complexity of the selected model. This paper proposes a criterion to select the tuning parameter for the SCAD method in multivariate generalized linear models, which is shown to be able to identify the true model consistently under some conditions. Simulation studies are conducted to support theoretical findings, and the Credit Score data is given to illustrate the proposed method.