On $\varepsilon$-Admissibility in High Dimension and Nonparametrics

TL;DR

This paper explores the concept of $\varepsilon$-admissibility as a more effective criterion than minimax rates for evaluating estimators in high-dimensional and nonparametric models, demonstrated through specific statistical models.

Contribution

It introduces and advocates for the use of $\varepsilon$-admissibility as a superior comparison tool in complex statistical estimation problems.

Findings

$\varepsilon$-admissibility provides better estimator comparison in high-dimensional models.

Demonstrated effectiveness in Poisson and Gaussian models.

Offers improved insights over traditional minimax rate analysis.

Abstract

In this paper, we discuss the use of $\varepsilon$-admissibility for estimation in high-dimensional and nonparametric statistical models. The minimax rate of convergence is widely used to compare the performance of estimators in high-dimensional and nonparametric models. However, it often works poorly as a criterion of comparison. In such cases, the addition of comparison by $\varepsilon$-admissibility provides a better outcome. We demonstrate the usefulness of $\varepsilon$-admissibility through high-dimensional Poisson model and Gaussian infinite sequence model, and present noble results.