  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.
