  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.
