Dimensionality determination: A thresholding double ridge ratio approach

Xuehu Zhu, Xu Guo, Tao Wang and Lixing Zhu

Computational Statistics & Data Analysis, 2020, vol. 146, issue C

Abstract: 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.

Keywords: Double ridge ratio criterion; Factor models; Local regression models; Sufficient dimension reduction; Thresholding (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:146:y:2020:i:c:s0167947320300013

DOI: 10.1016/j.csda.2020.106910

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