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

arXiv: https://arxiv.org/abs/1802.08405 · HTML: https://mlsanity.com/paper/1802.08405/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Feb 2018.

## Built on by (most cited first, 4 of 4)

- [Density Descent for Diversity Optimization](https://mlsanity.com/paper/2312.11331/) (2023)
- [Sample Complexities of Estimating Gumbel--Max Watermark Proportions with and without Reduction to Pivotal Statistics](https://mlsanity.com/paper/2607.00224/) (2026)
- [On the Efficient Implementation of High Accuracy Optimality of Profile Maximum Likelihood](https://mlsanity.com/paper/2210.06728/) (2022)
- [Testing Support Size More Efficiently Than Learning Histograms](https://mlsanity.com/paper/2410.18915/) (2024)

## Abstract (arXiv)

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.