Model averaging estimation for nonparametric varying-coefficient models with multiplicative heteroscedasticity

Xianwen Sun () and Lixin Zhang ()
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Xianwen Sun: Zhejiang University
Lixin Zhang: Zhejiang University

Statistical Papers, 2024, vol. 65, issue 3, No 9, 1375-1409

Abstract: Abstract In the last few years, frequentist model averaging has received more and more attention. However, the majority of related work focuses on the parametric model setup and devotes more energy to different mean structures but ignores the form of variance. In this paper, we consider a regression model with the mean being a varying-coefficient model and the variance being multiplicative heteroscedasticity and introduce a model averaging approach that uses the B-spline smoothing method to estimate unknown coefficient functions and obtains the estimators of unknown parameters in both the mean and variance functions of the model by the maximum likelihood method. The resulting model averaging estimator is proved to have asymptotic optimality under some regular conditions. Simulation experiments are conducted to compare the performance of our method with that of other common heteroscedasticity-robust model selection and model averaging methods under the finite-sample case. Our method is also verified in a real dataset.

Keywords: Model averaging; Nonparametric varying-coefficient models; Multiplicative heteroscedasticity; Prediction error; Maximum likelihood estimation; B-spline smoothing; 62F12; 62G08 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01447-8

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