Variable selection via thresholding

Ka Long Keith Ho

doi:10.1111/sjos.70032

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Variable selection via thresholding

2025-11-01

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Ka Long Keith Ho *

Hien D. Nguyen

DOI：10.1111/sjos.70032

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Abstract

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Variable selection comprises an important step in many modern statistical inference procedures. In the regression setting, when estimators cannot shrink irrelevant signals to zero, covariates without relationships to the response often manifest small but nonzero regression coefficients. The ad hoc procedure of discarding variables whose coefficients are smaller than some threshold is often employed in practice. We formally analyze a version of such thresholding procedures and develop a simple thresholding method that consistently estimates the set of relevant variables under mild regularity assumptions. Using this thresholding procedure, we propose a sparse, -consistent and asymptotically normal estimator whose nonzero elements do not exhibit shrinkage. The performance and applicability of our approach are examined via numerical studies of simulated and real data.

Keywords:

asymptotic normality

hard thresholding

regression analysis

sparse estimation

variable selection consistency