Good-Bootstrap: Simultaneous Confidence Intervals for Large Alphabet Distributions

Abstract

Abstract Simultaneous confidence intervals (SCI) for multinomial proportions are a corner stone in count data analysis and a key component in many applications. A variety of schemes were introduced over the years, mostly focusing on an asymptotic regime (where the sample is large), or a small sample regime, where the alphabet size is relatively small. In this work we introduce a new SCI framework which considers a large alphabet setup. Our proposed framework utilizes bootstrap sampling with the Good-Turing probability estimator as a plug-in distribution. We demonstrate the favorable performance of our proposed method in synthetic and real-world experiments. Importantly, we provide an exact analytical expression for the bootstraped statistic, which replaces the computationally costly sampling routine. Our proposed framework is publicly available at the first author's webpage.