Mixing partially linear regression models

In semiparametric modeling, often the main interest is on the parametric part. When a model selection step is performed to choose important variables for the parametric part, the selection uncertainty may or may not be negligible. If it is high, not only the identified model is not trustworthy but also the resulting estimator may have unnecessarily high variability. We propose model selection diagnostic measures both for variable selection and for regression estimation, which provide crucial information on reliability of the selected model and choice between model selection and model averaging for regression estimation. We study a model mixing method for estimating the linear function in a partially linear regression model and derive oracle inequalities that show the mixed estimators perform nearly as well as the best estimator from the candidate models. Simulation and data examples are encouraging.