Modified SEE variable selection for varying coefficient instrumental variable models

Abstract We consider the problem of variable selection for a class of varying coefficient models with instrumental variables. We focus on the case that some covariates are endogenous variables, and some auxiliary instrumental variables are available. An instrumental variable based variable selection procedure is proposed by using modified smooth-threshold estimating equations (SEEs). The proposed procedure can automatically eliminate the irrelevant covariates by setting the corresponding coefficient functions as zero, and simultaneously estimate the nonzero regression coefficients by solving the smooth-threshold estimating equations. The proposed variable selection procedure avoids the convex optimization problem, and is flexible and easy to implement. Simulation studies are carried out to assess the performance of the proposed variable selection method.

[1]  Masao Ueki,et al.  A note on automatic variable selection using smooth-threshold estimating equations , 2009 .

[2]  Zongwu Cai,et al.  Functional coefficient instrumental variables models , 2006 .

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

[4]  T. Schultz,et al.  Human capital, schooling and health. , 2003, Economics and human biology.

[5]  Instrumental regression in partially linear models , 2012 .

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

[7]  Heng Lian,et al.  Bias-corrected GEE estimation and smooth-threshold GEE variable selection for single-index models with clustered data , 2011, J. Multivar. Anal..

[8]  Lixing Zhu,et al.  Empirical Likelihood for a Varying Coefficient Model With Longitudinal Data , 2007 .

[9]  Runze Li,et al.  Tuning parameter selectors for the smoothly clipped absolute deviation method. , 2007, Biometrika.

[10]  J. Newhouse,et al.  Econometrics in outcomes research: the use of instrumental variables. , 1998, Annual review of public health.

[11]  Jianhua Z. Huang,et al.  Variable Selection in Nonparametric Varying-Coefficient Models for Analysis of Repeated Measurements , 2008, Journal of the American Statistical Association.

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

[13]  Masao Ueki,et al.  Automatic grouping using smooth-threshold estimating equations , 2011 .

[14]  David Card.  Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems , 2000 .

[15]  C. J. Stone,et al.  Optimal Global Rates of Convergence for Nonparametric Regression , 1982 .

[16]  Zongwu Cai,et al.  Partially varying coefficient instrumental variables models , 2012 .

[17]  Yingcun Xia,et al.  Shrinkage Estimation of the Varying Coefficient Model , 2008 .

[18]  Peixin Zhao,et al.  Variable selection for varying coefficient models with measurement errors , 2011 .

[19]  R. Tibshirani,et al.  Varying‐Coefficient Models , 1993 .