Model averaging estimation for generalized partially linear varying‐coefficient models

Abstract

Model averaging has long been used as a powerful approach to reduce the risk of model misspecification. However, there is little work on model averaging methods under generalized semiparametric models. In this article, we study model averaging in generalized partially linear varying‐coefficient models and propose a semiparametric model averaging estimation (SMAE) method for the canonical parameters. Specifically, we take the partially linear varying‐coefficient model as candidate models in which there is only one varying‐coefficient component. The different covariates could enjoy the benefit of matching the optimal degrees of freedom and each candidate model can take into account the confounding effects among predictors as well. Moreover, the weight choice criterion based on the Kullback–Leibler divergence is adopted to determine the weights. We prove that the corresponding model averaging estimator is asymptotically optimal under certain regularity conditions. Finally, some simulation studies and a real data analysis are conducted to compare with existing methods, and the results show that the proposed method has better out‐of‐sample performance.