Model averaging for varying-coefficient partially linear measurement error models

In a 2003 paper, Hjort and Claeskens proposed a framework for studying the limiting distributions and asymptotic risk properties of model average estimators under parametric models. They also suggested a simple method for constructing confidence intervals for the parameters of interest estimated by model averaging. The purpose of this paper is to broaden the scope of the aforementioned study to include a semi-parametric varying-coefficient partially linear measurement error model. Within this context, we develop a model averaging scheme for the unknowns, derive the model average estimator's asymptotic distribution, and develop a confidence interval procedure of the unknowns with an actual coverage probability that tends toward the nominal level in large samples. We further show that confidence intervals that are constructed based on the model average estimators are asymptotically the same as those obtained under the full model. A simulation study examines the finite sample performance of the model average estimators, and a real data analysis illustrates the application of the method in practice.