TY - JOUR
T1 - Dimensionality determination
T2 - A thresholding double ridge ratio approach
AU - Zhu, Xuehu
AU - Guo, Xu
AU - Wang, Tao
AU - Zhu, Lixing
N1 - Funding Information:
The authors are grateful to Drs. Bing Li, Wei Luo and Xinyu Zhang for providing partially codes. The research of Xuehu Zhu was supported by National Natural Science Foundation of China (No. 11601415, No. 61877049), China Postdoctoral Science Foundation (No. 2016M590934, No. 2017T100731) and was supported by “the Fundamental Research Funds for the Central Universities”. The research of Xu Guo was supported by National Natural Science Foundation of China (No. 11601227). The research of Tao Wang was supported, in part, by the National Natural Science Foundation of China (11601326, 11971017), National Key R&D Program of China (2018YFC0910500), Shanghai Municipal Science and Technology Major Project (2017SHZDZX01), and Neil Shen's SJTU Medical Research Fund. The research of Lixing Zhu was supported by a grant (HKBU123017/17) from the University Grants Council of Hong Kong, Hong Kong, China, and also partly supported by the National natural Science Foundation of China (No. 11671042). The authors thank the editor, the associate editor and two anonymous referees for their constructive comments and suggestions which led to a substantial improvement of an early manuscript.
Funding Information:
The authors are grateful to Drs. Bing Li, Wei Luo and Xinyu Zhang for providing partially codes. The research of Xuehu Zhu was supported by National Natural Science Foundation of China (No. 11601415 , No. 61877049 ), China Postdoctoral Science Foundation (No. 2016M590934 , No. 2017T100731 ) and was supported by “the Fundamental Research Funds for the Central Universities ”. The research of Xu Guo was supported by National Natural Science Foundation of China (No. 11601227 ). The research of Tao Wang was supported, in part, by the National Natural Science Foundation of China ( 11601326 , 11971017 ), National Key R&D Program of China ( 2018YFC0910500 ), Shanghai Municipal Science and Technology Major Project ( 2017SHZDZX01 ), and Neil Shen’s SJTU Medical Research Fund. The research of Lixing Zhu was supported by a grant ( HKBU123017/17 ) from the University Grants Council of Hong Kong , Hong Kong, China, and also partly supported by the National natural Science Foundation of China (No. 11671042 ). The authors thank the editor, the associate editor and two anonymous referees for their constructive comments and suggestions which led to a substantial improvement of an early manuscript.
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/6
Y1 - 2020/6
N2 - Underdetermination of model dimensionality (order) is a longstanding problem when existing eigendecomposition-based criteria are used. To alleviate this difficulty, we propose a thresholding double ridge ratio criterion in this paper. Unlike all existing eigendecomposition-based criteria, the proposed criterion can provide a consistent estimate even when there are several local minima. For illustration, we present the generic strategy with three important applications: dimension reduction in regressions with fixed and divergent dimensions; model checking with local alternative models; and ultra-high dimensional approximate factor models. Numerical studies are conducted to examine the finite sample performance of the proposed method and a real data example is analyzed for illustration.
AB - Underdetermination of model dimensionality (order) is a longstanding problem when existing eigendecomposition-based criteria are used. To alleviate this difficulty, we propose a thresholding double ridge ratio criterion in this paper. Unlike all existing eigendecomposition-based criteria, the proposed criterion can provide a consistent estimate even when there are several local minima. For illustration, we present the generic strategy with three important applications: dimension reduction in regressions with fixed and divergent dimensions; model checking with local alternative models; and ultra-high dimensional approximate factor models. Numerical studies are conducted to examine the finite sample performance of the proposed method and a real data example is analyzed for illustration.
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U2 - 10.1016/j.csda.2020.106910
DO - 10.1016/j.csda.2020.106910
M3 - Article
AN - SCOPUS:85079422950
SN - 0167-9473
VL - 146
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
M1 - 106910
ER -