arXiv (Cornell University)· 2013· Preprint
On the rate of convergence in Wasserstein distance of the empirical\n measure
- 970citations
- 2013year
Short summary
This paper establishes new non-asymptotic bounds and concentration inequalities for the convergence rate of empirical measures to their true distribution in Wasserstein distance, for any order p > 0 and dimension d >= 1.
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Key points
- Introduces new non-asymptotic $L^p$-bounds for Wasserstein distance convergence.
- Provides concentration inequalities for empirical measures.
- Results are valid for all $p>0$ and dimensions $d \geq 1$.
- Extends bounds to $\rho$-mixing sequences, Markov chains, and particle systems.
AI-generated from the title and abstract; the full text is not read.
Abstract
Let $\\mu_N$ be the empirical measure associated to a $N$-sample of a given\nprobability distribution $\\mu$ on $\\mathbb{R}^d$. We are interested in the rate\nof convergence of $\\mu_N$ to $\\mu$, when measured in the Wasserstein distance\nof order $p>0$. We provide some satisfying non-asymptotic $L^p$-bounds and\nconcentration inequalities, for any values of $p>0$ and $d\\geq 1$. We extend\nalso the non asymptotic $L^p$-bounds to stationary $\\rho$-mixing sequences,\nMarkov chains, and to some interacting particle systems.\n
The authors' abstract, as published at the source. arXiv (Cornell University), 2013 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics