Model averaging prediction for nonparametric varying-coefficient models with B-spline smoothing

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...

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Bibliographic Details
Published in:Statistical papers (Berlin, Germany) Germany), 2021-12, Vol.62 (6), p.2885-2905
Main Author: Xia, Xiaochao
Format: Article
Language:English
Subjects:
Approximation
Asymptotic methods
Asymptotic properties
Coefficients
Data analysis
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Insurance
Management
Mathematics and Statistics
Nonparametric statistics
Operations Research/Decision Theory
Optimization
Probability Theory and Stochastic Processes
Regular Article
Regularization methods
Smoothing
Statistics
Statistics for Business
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Summary: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.
ISSN:0932-5026
1613-9798
DOI:10.1007/s00362-020-01218-9