Local moment matching: A unified methodology for symmetric functional estimation and distribution estimation under Wasserstein distance

Understand

We present \emph{Local Moment Matching (LMM)}, a unified methodology for symmetric functional estimation and distribution estimation under Wasserstein distance.

• We construct an efficiently computable estimator that achieves the minimax rates in estimating the distribution up to permutation, and show that the plug-in approach of our unlabeled distribution estimator is "universal" in estimating symmetric functionals of discrete distributions.
• Instead of doing best polynomial approximation explicitly as in existing literature of functional estimation, the plug-in approach conducts polynomial approximation implicitly and attains the optimal sample complexity for the entropy, power sum and support size functionals.