广义线性模型下ERIC方法的调节参数选择

Tuning Parameter Selection Using ERIC Criterion in the Generalized Linear Model

变量选择是处理高维统计模型的基本方法,在回归模型的变量选择中SCAD惩罚函数不仅可以很好地选择出正确模型,同时还可以对参数进行估计,而且还具有oracle性质,但这些良好的性质是基于选择出一个合适的调节参数。目前国内关于调节参数选择方面大多是对于变量选择问题的研究,针对广义线性模型基于SCAD惩罚使用新方法 ERIC准则进行调节参数的选择,并证明在一定条件下经过该准则选择的模型具有一致性。模拟与实证分析结果表明,ERIC方法在选择调节参数方面优于传统的CV准则、AIC准则和BIC准则。

Variable selection is the basic method to deal with high-dimensional statistical model.Smoothly clipped absolute deviation(SCAD)is a good kind of penalty function in the variable selection of regression model.It not only is a good way to choose the true model,but also can be used to estimate the parameters.Besides it also has oracle property.However,these good properties are based on the selection of a suitable tuning parameter.Only when the selection of the tuning parameters is appropriate,can SCAD penalty get a good estimated result.In this paper,we propose the extended regularized information criterion(ERIC)for choosing the tuning parameters based on SCAD penalty in the generalized linear model.At the same time,we prove that the model selected by this criterion is consistent under certain conditions.