A Mallows-Type Model Averaging Estimator for the Varying-Coefficient Partially Linear Model

ABSTRACT

In the last decade, significant theoretical advances have been made in the area of frequentist model averaging (FMA); however, the majority of this work has emphasized parametric model setups. This article considers FMA for the semiparametric varying-coefficient partially linear model (VCPLM), which has gained prominence to become an extensively used modeling tool in recent years. Within this context, we develop a Mallows-type criterion for assigning model weights and prove its asymptotic optimality. A simulation study and a real data analysis demonstrate that the FMA estimator that arises from this criterion is vastly preferred to information criterion score-based model selection and averaging estimators. Our analysis is complicated by the fact that the VCPLM is subject to uncertainty arising not only from the choice of covariates, but also whether the covariate should enter the parametric or nonparametric parts of the model. Supplementary materials for this article are available online.

Keywords:

• Asymptotic optimality
• Heteroscedasticity
• Mallows criterion
• Model averaging
• Varying-coefficient partially linear model

Acknowledgment

The authors thank the editor, associate editor, and two referees for insightful comments that have helped improve the quality of the article. The usual disclaimer applies.

Additional information

Funding

Wan’s work was supported by a Strategic Grant from the City University of Hong Kong (Grant no. 7004786). Zhang’s and Zou’s work was supported by the following funding bodies: National Natural Science Foundation of China (Grant nos. 71522004 (Zhang), 11471324 (Zhang), 71631008 (Zhang), 11331011 (Zou), and 11529101 (Zou)) and the Ministry of Science and Technology of China (Grant no. 2016YFB0502301 (Zou)).