A Unified Maximum Likelihood Approach for Optimal Distribution Property Estimation

Understand

The advent of data science has spurred interest in estimating properties of distributions over large alphabets.

• Fundamental symmetric properties such as support size, support coverage, entropy, and proximity to uniformity, received most attention, with each property estimated using a different technique and often intricate analysis tools.
• We prove that for all these properties, a single, simple, plug-in estimator---profile maximum likelihood (PML)---performs as well as the best specialized techniques.
• This raises the possibility that PML may optimally estimate many other symmetric properties.