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The advent of data science has spurred interest in estimating properties ofdistributions over large alphabets. Fundamental symmetric properties such assupport size, support coverage, entropy, and proximity to uniformity, receivedmost attention, with each property estimated using a different technique andoften intricate analysis tools.  We prove that for all these properties, a single, simple, plug-inestimator---profile maximum likelihood (PML)---performs as well as the bestspecialized techniques. This raises the possibility that PML may optimallyestimate many other symmetric properties.

A Unified Maximum Likelihood Approach for Optimal Distribution Property Estimation