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

02/23/2018
by   Yanjun Han, et al.
0

We present 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

09/17/2019

Minimax Confidence Intervals for the Sliced Wasserstein Distance

The Wasserstein distance has risen in popularity in the statistics and m...
11/08/2019

Unified Sample-Optimal Property Estimation in Near-Linear Time

We consider the fundamental learning problem of estimating properties of...
06/10/2019

The Broad Optimality of Profile Maximum Likelihood

We study three fundamental statistical-learning problems: distribution e...
11/28/2018

Minimax Optimal Additive Functional Estimation with Discrete Distribution

This paper addresses a problem of estimating an additive functional give...
08/27/2020

On the High Accuracy Limitation of Adaptive Property Estimation

Recent years have witnessed the success of adaptive (or unified) approac...
06/26/2022

The Sketched Wasserstein Distance for mixture distributions

The Sketched Wasserstein Distance (W^S) is a new probability distance sp...
09/19/2022

Theory of functional principal components analysis for discretely observed data

For discretely observed functional data, estimating eigenfunctions with ...