Variable Selection in Measurement Error Models Via Penalized Estimating

Compared with ordinary regression models, the computational cost for estimating parame-ters in general measurement error models is often much more expensive because the estimation procedures typically require solving integral equations. In addition, natural criteria functions are often unavailable for general measurement error models. Thus, the traditionally best vari-able selection procedures become infeasible in the measurement error models context. In this paper, we develop a new framework for variable selection in measurement error models via penalized estimating equations. We first propose a new class of variable selection procedures for general parametric measurement error models and for general semiparametric measurement error models, and study the asymptotic properties of the proposed procedures. Then, under certain regularity conditions and with a properly chosen regularization parameter, we demon-strate that the proposed procedure performs as well as an oracle procedure. We assess the finite sample performance by Monte Carlo simulation studies and illustrate the proposed methodology through the empirical analysis of a real data set.