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

Keisuke Yano; Fumiyasu Komaki

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arXiv · 1708.03751

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

Keisuke Yano·Fumiyasu Komaki

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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.

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Keisuke Yano, Fumiyasu Komaki. 2017-08-12. On $\varepsilon$-Admissibility in High Dimension and Nonparametrics. https://arxiv.org/abs/1708.03751

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