@inproceedings{d4ec2950879a4a198d594175c39f49e5,
title = "Nonparametric Kullback-Liebler Divergence Estimation Using M-Spacing",
abstract = "Entropy of a random variable with unknown distribution function can be estimated nonparametrically by spacing methods when independent and identically distributed (i.i.d.) observations of the random variable are available. We extend the classical entropy estimator based on sample spacing to define an m-spacing estimator for the Kullback-Liebler (KL) divergence between two i.i.d. observations with unknown distribution functions, which can be applied to measure discrepancy between real-world system output and simulation output as well as between two simulators' outputs. We show that the proposed estimator converges almost surely to the true KL divergence as the numbers of outputs collected from both systems increase under mild conditions and discuss the required choices for m and the simulation output sample size as functions of the real-world sample size. Additionally, we show Central Limit Theorems for the proposed estimator with appropriate scaling.",
author = "Linyun He and Eunhye Song",
note = "Publisher Copyright: {\textcopyright} 2021 IEEE.; 2021 Winter Simulation Conference, WSC 2021 ; Conference date: 12-12-2021 Through 15-12-2021",
year = "2021",
doi = "10.1109/WSC52266.2021.9715376",
language = "English (US)",
series = "Proceedings - Winter Simulation Conference",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
booktitle = "2021 Winter Simulation Conference, WSC 2021",
address = "United States",
}