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

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.