Minimax estimation of the L1 distance

@article{Jiao2016MinimaxEO,
  title={Minimax estimation of the L1 distance},
  author={J. Jiao and Y. Han and T. Weissman},
  journal={2016 IEEE International Symposium on Information Theory (ISIT)},
  year={2016},
  pages={750-754}
}
  • J. Jiao, Y. Han, T. Weissman
  • Published 2016
  • Mathematics, Computer Science
  • 2016 IEEE International Symposium on Information Theory (ISIT)
  • We consider the problem of estimating the L1 distance between two discrete probability measures P and Q from empirical data in a nonasymptotic and large alphabet setting. We construct minimax rate-optimal estimators for L1(P,Q) when Q is either known or unknown, and show that the performance of the optimal estimators with n samples is essentially that of the Maximum Likelihood Estimators (MLE) with n ln n samples. Hence, we demonstrate that the effective sample size enlargement phenomenon… CONTINUE READING
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