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A Unified Maximum Likelihood Approach for Estimating Symmetric Properties of Discrete Distributions

2020-03-09 | |  62 |   34 |   0

Abstract

Symmetric distribution properties such as support size, support coverage, entropy, and proximity to uniformity, arise in many applications. Recently, researchers applied different estimators and analysis tools to derive asymptotically sample-optimal approximations for each of these properties. We show that a single, simple, plug-in estimator—profile maximum likelihood (PML)– is sample competitive for all symmetric properties, and in particular is asymptotically sampleoptimal for all the above properties.

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