Quasi-likelihood Bridge estimators for high-dimensional generalized linear models

ABSTRACT In this article, we consider the variable selection and estimation for high-dimensional generalized linear models when the number of parameters diverges with the sample size. We propose a penalized quasi-likelihood function with the bridge penalty. The consistency and the Oracle property of the quasi-likelihood bridge estimators are obtained. Some simulations and a real data analysis are given to illustrate the performance of the proposed method.

[1]  Jin-Guan Lin,et al.  Asymptotic properties of maximum quasi-likelihood estimators in generalized linear models with adaptive designs , 2012 .

[2]  P. McCullagh.  Quasi-Likelihood Functions , 1983 .

[3]  H. Zou,et al.  Regularization and variable selection via the elastic net , 2005 .

[4]  H. Zou.  The Adaptive Lasso and Its Oracle Properties , 2006 .

[5]  Arthur E. Hoerl,et al.  Ridge Regression: Biased Estimation for Nonorthogonal Problems , 2000, Technometrics.

[6]  R. W. Wedderburn.  Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method , 1974 .

[7]  Chengdong Wei,et al.  Asymptotic normality and strong consistency of maximum quasi-likelihood estimates in generalized linear models , 2006 .

[8]  Y. Chang,et al.  Sequential confidence regions of generalized linear models with adaptive designs , 2001 .

[9]  J. Horowitz,et al.  Asymptotic properties of bridge estimators in sparse high-dimensional regression models , 2008, 0804.0693.

[10]  T. Hastie,et al.  [A Statistical View of Some Chemometrics Regression Tools]: Discussion , 1993 .

[11]  Lili Yue,et al.  Rate of strong consistency of quasi maximum likelihood estimate in generalized linear models , 2004 .

[12]  Lixin Song,et al.  Bridge estimation for generalized linear models with a diverging number of parameters , 2010 .

[13]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[14]  C. Xiru,et al.  Adaptive quasi-likelihood estimate in generalized linear models , 2005 .

[15]  Wenjiang J. Fu,et al.  Asymptotics for lasso-type estimators , 2000 .

[16]  Kani Chen,et al.  Strong consistency of maximum quasi-likelihood estimators in generalized linear models with fixed and adaptive designs , 1999 .

[17]  Jianqing Fan,et al.  A Selective Overview of Variable Selection in High Dimensional Feature Space. , 2009, Statistica Sinica.

[18]  Chenlei Leng,et al.  Shrinkage tuning parameter selection with a diverging number of parameters , 2008 .

[19]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[20]  Jianqing Fan,et al.  Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties , 2001 .

[21]  Terence Tao,et al.  The Dantzig selector: Statistical estimation when P is much larger than n , 2005, math/0506081.

[22]  V. P. Godambe.  Conditional likelihood and unconditional optimum estimating equations , 1976 .

[23]  J. Friedman,et al.  A Statistical View of Some Chemometrics Regression Tools , 1993 .

[24]  Yuan-chin Ivan Chang,et al.  Strong consistency of maximum quasi-likelihood estimate in generalized linear models via a last time , 1999 .

[25]  Ashutosh Kumar Singh,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction , 2010 .

[26]  V. P. Godambe.  An Optimum Property of Regular Maximum Likelihood Estimation , 1960 .