Description

Book Synopsis
This work is devoted to the study of rates of convergence of the empirical measures $\mu_{n} = \frac {1}{n} \sum_{k=1}^n \delta_{X_k}$, $n \geq 1$, over a sample $(X_{k})_{k \geq 1}$ of independent identically distributed real-valued random variables towards the common distribution $\mu$ in Kantorovich transport distances $W_p$.

Table of Contents
  • Introduction
  • Generalities on Kantorovich transport distances
  • The Kantorovich distance $W_1(\mu _n, \mu )$
  • Order statistics representations of $W_p(\mu _n, \mu )$
  • Standard rate for $\mathbb{E} (W_p^p(\mu _n,\mu ))$
  • Sampling from log-concave distributions
  • Miscellaneous bounds and results
  • Appendix A. Inverse distribution functions
  • Appendix B. Beta distributions
  • Bibliography.

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      A Paperback by Sergey Bobkov, Michel Ledoux

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        Publisher: MP-AMM American Mathematical
        Publication Date: 12/30/2019 12:00:00 AM
        ISBN13: 9781470436506, 978-1470436506
        ISBN10: 1470436507

        Description

        Book Synopsis
        This work is devoted to the study of rates of convergence of the empirical measures $\mu_{n} = \frac {1}{n} \sum_{k=1}^n \delta_{X_k}$, $n \geq 1$, over a sample $(X_{k})_{k \geq 1}$ of independent identically distributed real-valued random variables towards the common distribution $\mu$ in Kantorovich transport distances $W_p$.

        Table of Contents
        • Introduction
        • Generalities on Kantorovich transport distances
        • The Kantorovich distance $W_1(\mu _n, \mu )$
        • Order statistics representations of $W_p(\mu _n, \mu )$
        • Standard rate for $\mathbb{E} (W_p^p(\mu _n,\mu ))$
        • Sampling from log-concave distributions
        • Miscellaneous bounds and results
        • Appendix A. Inverse distribution functions
        • Appendix B. Beta distributions
        • Bibliography.

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