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Central Limit Theorem on Symmetric Kullback-Leibler (KL) Divergence

Helder Rojas, Artem Logachov

Abstract

In this paper we provide an asymptotic theory for the symmetric version of the Kullback--Leibler (KL) divergence. We define a estimator for this divergence and study its asymptotic properties. In particular, we prove Law of Large Numbers (LLN) and the convergence to the normal law in the Central Limit Theorem (CLT) using this estimator.

Central Limit Theorem on Symmetric Kullback-Leibler (KL) Divergence

Abstract

In this paper we provide an asymptotic theory for the symmetric version of the Kullback--Leibler (KL) divergence. We define a estimator for this divergence and study its asymptotic properties. In particular, we prove Law of Large Numbers (LLN) and the convergence to the normal law in the Central Limit Theorem (CLT) using this estimator.
Paper Structure (3 sections, 124 equations)

This paper contains 3 sections, 124 equations.

Table of Contents

  1. Introduction
  2. Main results
  3. Auxiliary results