Structure identification for varying coefficient models with measurement errors based on kernel smoothing

Abstract

Measurement error data are often encountered in a broad spectrum of scientific fields, including engineering, economics, biomedical sciences and epidemiology. Simply ignoring the measurement errors would result in biased estimators. Combining the local kernel smoothing and the SCAD approach, this paper proposes a bias-corrected penalized method to capture the underlying structure of varying coefficient models with measurement errors. We show that, under the proper choice of tuning parameters and some regular conditions, the proposed method can consistently remove all the unimportant variables and separate the constant effects and varying effects. The corresponding algorithm is also developed to compute the estimates using the local quadratic approximation. Simulation studies are conducted to assess the finite sample performance of the proposed method.