Minimax Estimation of the $L_1$ Distance

@article{Jiao2018MinimaxEO,
  title={Minimax Estimation of the \$L_1\$ Distance},
  author={J. Jiao and Y. Han and T. Weissman},
  journal={IEEE Trans. Inf. Theory},
  year={2018},
  volume={64},
  pages={6672-6706}
}
  • J. Jiao, Y. Han, T. Weissman
  • Published 2018
  • Mathematics, Computer Science
  • IEEE Trans. Inf. Theory
  • We consider the problem of estimating the $L_{1}$ distance between two discrete probability measures $P$ and $Q$ from empirical data in a nonasymptotic and large alphabet setting. When $Q$ is known and one obtains $n$ samples from $P$ , we show that for every $Q$ , the minimax rate-optimal estimator with $n$ samples achieves performance comparable to that of the maximum likelihood estimator with $n\ln n$ samples. When both $P$ and $Q$ are unknown, we construct minimax rate-optimal estimators… CONTINUE READING
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