Moderate deviations for a nonparametric estimator of sample coverage

TL;DR

This paper establishes moderate deviation principles for Good's coverage estimator, providing theoretical insights into its probabilistic behavior and applications in hypothesis testing and confidence interval construction.

Contribution

It introduces the first moderate deviation principles for Good's coverage estimator, enhancing understanding of its probabilistic properties and practical utility.

Findings

Established moderate deviation principle for Good's coverage estimator.

Proved self-normalized moderate deviation principle.

Applied results to hypothesis testing and confidence intervals.

Abstract

In this paper, we consider moderate deviations for Good's coverage estimator. The moderate deviation principle and the self-normalized moderate deviation principle for Good's coverage estimator are established. The results are also applied to the hypothesis testing problem and the confidence interval for the coverage.