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

Abstract

In this paper, we discuss the use of $\epsilon$-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 $\epsilon$-admissibility provides a better outcome. We demonstrate the usefulness of $\epsilon$-admissibility through high-dimensional Poisson model and Gaussian infinite sequence model, and present noble results.

22 pages

References in corpus (1)

• A note on the approximate admissibility of regularized estimators in the Gaussian sequence model