Thinning and information projections

Peter Harremoës; Oliver T Johnson; Ioannis Kontoyiannis

Thinning and information projections

Peter Harremoës
, Oliver T Johnson
, Ioannis Kontoyiannis

Research output: Working paper

Abstract

In this paper we establish lower bounds on information divergence of a distribution on the integers from a Poisson distribution. These lower bounds are tight and in the cases where a rate of convergence in the Law of Thin Numbers can be computed the rate is determined by the lower bounds proved in this paper. General techniques for getting lower bounds in terms of moments are developed. The results about lower bound in the Law of Thin Numbers are used to derive similar results for the Central Limit Theorem.

Original language	English
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Number of pages	11
Publication status	Submitted - 17 Jan 2016

Keywords

Information divergence
Poisson-Charlier polynomials
Poisson distribution
Thinning

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title = "Thinning and information projections",

abstract = "In this paper we establish lower bounds on information divergence of a distribution on the integers from a Poisson distribution. These lower bounds are tight and in the cases where a rate of convergence in the Law of Thin Numbers can be computed the rate is determined by the lower bounds proved in this paper. General techniques for getting lower bounds in terms of moments are developed. The results about lower bound in the Law of Thin Numbers are used to derive similar results for the Central Limit Theorem.",

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TY - UNPB

T1 - Thinning and information projections

AU - Harremoës, Peter

AU - Johnson, Oliver T

AU - Kontoyiannis, Ioannis

PY - 2016/1/17

Y1 - 2016/1/17

N2 - In this paper we establish lower bounds on information divergence of a distribution on the integers from a Poisson distribution. These lower bounds are tight and in the cases where a rate of convergence in the Law of Thin Numbers can be computed the rate is determined by the lower bounds proved in this paper. General techniques for getting lower bounds in terms of moments are developed. The results about lower bound in the Law of Thin Numbers are used to derive similar results for the Central Limit Theorem.

AB - In this paper we establish lower bounds on information divergence of a distribution on the integers from a Poisson distribution. These lower bounds are tight and in the cases where a rate of convergence in the Law of Thin Numbers can be computed the rate is determined by the lower bounds proved in this paper. General techniques for getting lower bounds in terms of moments are developed. The results about lower bound in the Law of Thin Numbers are used to derive similar results for the Central Limit Theorem.

KW - Information divergence

KW - Poisson-Charlier polynomials

KW - Poisson distribution

KW - Thinning

UR - http://arxiv.org/abs/1601.04255

M3 - Working paper

BT - Thinning and information projections

PB - Institute of Electrical and Electronics Engineers (IEEE)

ER -

Thinning and information projections

Abstract

Keywords

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