Multifold Cross-Validation Model Averaging for Generalized Additive Partial Linear Models

Ze Chen, Jun Liao, Wangli Xu, Yuhong Yang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Generalized Additive Partial Linear Models (GAPLMs) are appealing for model interpretation and prediction. However, for GAPLMs, the covariates and the degree of smoothing in the nonparametric parts are often difficult to determine in practice. To address this model selection uncertainty issue, we develop a computationally feasible Model Averaging (MA) procedure. The model weights are data-driven and selected based on multifold Cross-Validation (CV) (instead of leave-one-out) for computational saving. When all the candidate models are misspecified, we show that the proposed MA estimator for GAPLMs is asymptotically optimal in the sense of achieving the lowest possible Kullback-Leibler loss. In the other scenario where the candidate model set contains at least one quasi-correct model, the weights chosen by the multifold CV are asymptotically concentrated on the quasi-correct models. As a by-product, we propose a variable importance measure to quantify the importances of the predictors in GAPLMs based on the MA weights. It is shown to be able to asymptotically identify the variables in the true model. Moreover, when the number of candidate models is very large, a model screening method is provided. Numerical experiments show the superiority of the proposed MA method over some existing model averaging and selection methods. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)1649-1659
Number of pages11
JournalJournal of Computational and Graphical Statistics
Issue number4
StatePublished - 2023

Bibliographical note

Publisher Copyright:
© 2023 American Statistical Association and Institute of Mathematical Statistics.


  • Asymptotic optimality
  • Generalized additive partial linear models
  • Multifold cross-validation criterion
  • Over-consistency of weights
  • Variable importance


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