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A NEW STUDY ON ASYMPTOTIC OPTIMALITY OF LEAST SQUARES MODEL AVERAGING

Published online by Cambridge University Press:  14 April 2020

Xinyu Zhang
Xinyu Zhang*
Affiliation:
Academy of Mathematics and Systems Science Chinese Academy of Sciences
*
Address correspondence to Xinyu Zhang, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; e-mail: xinyu@amss.ac.cn.
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Abstract

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In this article, we present a comprehensive study of asymptotic optimality of least squares model averaging methods. The concept of asymptotic optimality is that in a large-sample sense, the method results in the model averaging estimator with the smallest possible prediction loss among all such estimators. In the literature, asymptotic optimality is usually proved under specific weights restriction or using hardly interpretable assumptions. This article provides a new approach to proving asymptotic optimality, in which a general weight set is adopted, and some easily interpretable assumptions are imposed. In particular, we do not impose any assumptions on the maximum selection risk and allow a larger number of regressors than that of existing studies.

Information

Type
MISCELLANEA
Information
Econometric Theory , Volume 37 , Issue 2 , April 2021, pp. 388 - 407
Copyright
© Cambridge University Press 2020

Footnotes

We thank two anonymous referees, the Co-Editor, the Editor Peter C.B. Phillips, Tie Xie, and Jiahui Zou for many constructive comments and suggestions. Zhang gratefully acknowledges the research support from National Natural Science Foundation of China (grant numbers 71925007, 71631008, and 11688101). All errors remain the author.

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