Central limit theorem and convergence to stable laws in Mallows distance

By Oliver Johnson, Richard J. Samworth. 2004

56 citations recorded by the source corpus.

We give a new proof of the classical Central Limit Theorem, in the Mallows (L r -Wasserstein) distance. Our proof is elementary in the sense that it does not require complex analysis, but rather makes use of a simple subadditive inequality related to this metric. The key is to analyse the case where equality holds. We provide some results concerning rates of convergence. We also consider convergence to stable distributions, and obtain a bound on the rate of such convergence.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a3d2014cddfc6378acbfe0d2941b9a1812feaa23

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Citations in the corpus

Statistical Aspects of Wasserstein Distances (2018, background): “Johnson & Samworth (2005) obtain rates of convergence for the central limit theorem, and more generally, for convergence to stable laws.”
Inference for empirical Wasserstein distances on finite spaces (2016, methodology): “…has mainly been used as a tool to prove weak convergence in the context of limit laws (e.g. Bickel and Freedman (1981), Shorack and Wellner (1986), Johnson and Samworth (2005), Dümbgen et al. (2011) and Dorea and Ferreira (2012)) as it metrizes weak convergence together with convergence of…”
Empirical optimal transport on countable metric spaces: Distributional limits and statistical applications (2017, background): “…measures on (X , d) together with convergence of its first p moments and has become a standard tool in probability, e.g., to study limit laws (e.g., Johnson and Samworth (2005); Rachev and Rüschendorf (1994); Shorack and Wellner (1986)), to derive bounds for Monte Carlo computation schemes such…”