Characterization and estimation of high dimensional sparse regression parameters under linear inequality constraints

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2302.01974.pdf (8.73 MB)

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https://arxiv.org/abs/2302.01974

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https://doi.org/10.48550/arXiv.2302.01974
 http://hdl.handle.net/11603/26932

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UMBC Mathematics and Statistics Department
UMBC Faculty Collection

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https://orcid.org/0000-0001-6361-8295

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2023-02-03

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journal articles
preprints
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This work was written as part of one of the author's official duties as an Employee of the United States Government and is therefore a work of the United States Government. In accordance with 17 U.S.C. 105, no copyright protection is available for such works under U.S. Law.
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Abstract

Modern statistical problems often involve such linear inequality constraints on model parameters. Ignoring natural parameter constraints usually results in less efficient statistical procedures. To this end, we define a notion of ‘sparsity’ for such restricted sets using lower-dimensional features. We allow our framework to be flexible so that the number of restrictions may be higher than the number of parameters. One such situation arise in estimation of monotone curve using a non parametric approach e.g. splines. We show that the proposed notion of sparsity agrees with the usual notion of sparsity in the unrestricted case and proves the validity of the proposed definition as a measure of sparsity. The proposed sparsity measure also allows us to generalize popular priors for sparse vector estimation to the constrained case.