Asymptotics for Estimating a Diverging Number of Parameters -- With and Without Sparsity

MCML Authors

Thomas Nagler

Prof. Dr.

Principal Investigator

Computational Statistics & Data Science

Abstract

We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized estimation settings. The conditions are weak and accommodate a broad class of estimation problems, including ones with non-convex and group structured penalties. The wide applicability of the results is illustrated through diverse examples, including generalized linear models, multi-sample inference, and stepwise estimation procedures.

misc

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Preprint

Nov. 2024

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Authors

J. Gauss • T. Nagler

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Links

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Research Area

 A1 | Statistical Foundations & Explainability