Penalized estimating functions and variable selection in semiparametric regression models

We propose a general strategy for variable selection in semiparametric regression models by penalizing appropriate estimating functions. Important applications include semiparametric linear regression with censored responses and semiparametric regression with missing pre dictors. Unlike the existing penalized maximum likelihood estimators, the proposed penalized estimating functions may not pertain to the derivatives of any objective functions and may be discrete in the regression coefficients. We establish a general asymptotic theory for penalized estimating functions and present suitable numerical algorithms to implement the proposed estimators. In addition, we develop a resampling technique to estimate the variances of the estimated regression coefficients when the asymptotic variances cannot be evaluated directly. Simulation studies demonstrate that the proposed methods perform well in variable selection and variance estimation. We illustrate our methods using data from the Paul Converdell Stoke Registry. KEY WORDS: Accelerated failure time model; Buckley-James estimator; Censoring; Least absolute shrinkage and selection operator; Least squares; Linear regression; Missing data; Smoothly clipped absolute deviation.