Semiparametric Generalized Linear Model With N-P Dimension

Penalized likelihood methods are fundamental to ultrahigh dimensional variable selection.In the past two decades,The regularization approach for variable selection has been well developed,but there are very few studies on regularization of pairwise pseudo likelihood with U-statistics structure at present.In this paper,we first introduce the Hoeffding inequality for U-statistics whose kernel is unbounded.Secondly,when the sample size and parameter dimension tend to be infinite,we prove that the regularized estimators of regression coe cients in semi-parametric generalized linear model is not only sparse,but also consistent and asymptotically normal.Finally,We verify the practicability of regularized estimators in semiparametric generalized linear model through comprehensive simulation and real data analysis.Our conclusions apply not only to LASSO,but also to non-concave penalties such as SCAD and MCP.