Abstract
Model averaging has been demonstrated as a powerful tool in statistical prediction over the past decade. However, a majority of related works focus on the parametric model averaging. In this paper, we propose a model averaging estimation under nonparametric varying-coefficient models. Differing from existing works, our proposal concentrates on the development of the B-spline approximation to nonparametric varying coefficient functions for model average estimator, rendering the computational burden more cheaply than the kernel smoothing based estimator. Furthermore, our procedure is asymptotically optimal under mild conditions. The asymptotic optimality established in current paper is in terms of conditional quadratic loss function when the variance of model error is known or unknown, respectively. Three different cases of candidate models are considered. Extensive simulations are carried out to evaluate the finite-sample performance of our estimator. A real data is analyzed for illustration as well.
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Acknowledgements
We thank the Editor and two anonymous reviewers for their constructive comments and suggestions, which greatly improves the current work. This work was supported by National Natural Science Foundation of China (Grant No. 11801202).
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Xia, X. Model averaging prediction for nonparametric varying-coefficient models with B-spline smoothing. Stat Papers 62, 2885–2905 (2021). https://doi.org/10.1007/s00362-020-01218-9
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DOI: https://doi.org/10.1007/s00362-020-01218-9