A Scalable Frequentist Model Averaging Method
Zhu, Rong1; Wang, Haiying2; Zhang, Xinyu3; Liang, Hua4
AbstractFrequentist model averaging is an effective technique to handle model uncertainty. However, calculation of the weights for averaging is extremely difficult, if not impossible, even when the dimension of the predictor vector, p, is moderate, because we may have 2(p) candidate models. The exponential size of the candidate model set makes it difficult to estimate all candidate models, and brings additional numeric errors when calculating the weights. This article proposes a scalable frequentist model averaging method, which is statistically and computationally efficient, to overcome this problem by transforming the original model using the singular value decomposition. The method enables us to find the optimal weights by considering at most p candidate models. We prove that the minimum loss of the scalable model averaging estimator is asymptotically equal to that of the traditional model averaging estimator. We apply the Mallows and Jackknife criteria to the scalable model averaging estimator and prove that they are asymptotically optimal estimators. We further extend the method to the high-dimensional case (i.e., p >= n). Numerical studies illustrate the superiority of the proposed method in terms of both statistical efficiency and computational cost.
KeywordAsymptotic optimality High-dimensional data Jackknife criterion Mallows criterion Singular value decomposition
Indexed BySCI
Funding ProjectNNSF of China[11301514] ; NNSF of China[71532013] ; Shanghai Municipal Science and Technology Major Project[2018SHZDZX01] ; 111 Project[B18015] ; NNSF grant[71925007] ; NNSF grant[72091212] ; NNSF grant[12288201] ; CAS Project for Young Scientists in Basic Research[YSBR-008] ; NSF[2105571]
WOS Research AreaBusiness & Economics ; Mathematical Methods In Social Sciences ; Mathematics
WOS SubjectEconomics ; Social Sciences, Mathematical Methods ; Statistics & Probability
WOS IDWOS:000863731800001
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Document Type期刊论文
Corresponding AuthorLiang, Hua
Affiliation1.Fudan Univ, Inst Sci & Technol Brain Inspired Intelligence, Shanghai, Peoples R China
2.Univ Connecticut, Dept Stat, Storrs, CT 06269 USA
3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
4.George Washington Univ, Dept Stat, Washington, DC 20052 USA
Recommended Citation
GB/T 7714
Zhu, Rong,Wang, Haiying,Zhang, Xinyu,et al. A Scalable Frequentist Model Averaging Method[J]. JOURNAL OF BUSINESS & ECONOMIC STATISTICS,2022:10.
APA Zhu, Rong,Wang, Haiying,Zhang, Xinyu,&Liang, Hua.(2022).A Scalable Frequentist Model Averaging Method.JOURNAL OF BUSINESS & ECONOMIC STATISTICS,10.
MLA Zhu, Rong,et al."A Scalable Frequentist Model Averaging Method".JOURNAL OF BUSINESS & ECONOMIC STATISTICS (2022):10.
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