## Abstract

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. We construct minimax rate-optimal estimators for L_{1}(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, discovered and discussed in Jiao et al. (2015), holds for this problem as well. However, the construction of optimal estimators for L_{1}(P,Q) requires new techniques and insights outside the scope of the Approximation methodology of functional estimation in Jiao et al. (2015).

Original language | English (US) |
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Title of host publication | Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 750-754 |

Number of pages | 5 |

ISBN (Electronic) | 9781509018062 |

DOIs | |

State | Published - Aug 10 2016 |

Event | 2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain Duration: Jul 10 2016 → Jul 15 2016 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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Volume | 2016-August |

ISSN (Print) | 2157-8095 |

### Other

Other | 2016 IEEE International Symposium on Information Theory, ISIT 2016 |
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Country/Territory | Spain |

City | Barcelona |

Period | 7/10/16 → 7/15/16 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

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