Econometric Theory· 2026Q1
PROXIMAL ESTIMATION AND INFERENCE
- 3citations
- Q1SCImago
- 2026year
Short summary
A new convex-analytic framework constructs penalized estimators by applying proximal operators to benchmark estimators, achieving the oracle property under both regular and irregular designs for the first time.
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Key points
- Introduces a convex-analytic framework for penalized estimators using proximal operators on benchmark estimators.
- Establishes general finite-sample properties and unified asymptotic distribution results.
- Provides tractable conditions for oracle selection and asymptotic efficiency.
- Achieves the oracle property for penalized estimators in linear regression, even with irregular and singular designs, for the first time.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We develop a convex-analytic framework for constructing and analyzing a broad class of penalized estimators. Our method defines penalized estimators by applying proximal operators to benchmark estimators, rather than by penalizing the benchmark criterion itself. We establish general finite-sample properties, derive unified asymptotic distribution results, and provide tractable conditions for oracle selection and oracle asymptotic efficiency. We then apply the framework to linear regression with irregular designs, including singular and nearly-singular cases. In this setting, where the coefficient vector need not be point identified, we motivate the Ridgeless estimand as the inferential target, construct a n $\sqrt {n}$ StartRoot n EndRoot -consistent modified Ridgeless benchmark estimator, and combine it with adaptive proximal penalization to obtain, to the best of our knowledge, the first penalized estimator achieving the oracle property under both regular and irregular designs.
The authors' abstract, as published at the source. Econometric Theory, 2026 · DOI ↗
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Field: Statistics and Probability
Statistics and ProbabilityMathematics