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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

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Normal Laws for Two Entropy Estimators on Infinite Alphabets.

Chen Chen¹, Michael Grabchak¹, Ann Stewart¹

¹Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA.

Entropy (Basel, Switzerland)

|December 3, 2020

Summary

This summary is machine-generated.

This study establishes conditions for two entropy estimators, the Miller-Madow and jackknife methods, to achieve asymptotic normality on infinite alphabets. These findings are crucial for statistical inference in information theory.

Keywords:

Miller–Madow estimator asymptotic normality entropy jackknife estimator nonparametric estimator

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Area of Science:

Information Theory
Statistical Inference
Probability Theory

Background:

Entropy estimation is fundamental in information theory.
Countably infinite alphabets present unique challenges for statistical estimation.
Asymptotic normality is a key property for validating statistical estimators.

Purpose of the Study:

To derive sufficient conditions for the asymptotic normality of entropy estimators.
To analyze the Miller-Madow and jackknife estimators specifically.
To extend these analyses to the context of countably infinite alphabets.

Main Methods:

Mathematical analysis of statistical estimators.
Derivation of asymptotic properties.
Application of probability theory to information measures.

Main Results:

Sufficient conditions for the asymptotic normality of the Miller-Madow estimator were established.
Sufficient conditions for the asymptotic normality of the jackknife estimator were established.
These conditions are applicable to countably infinite alphabets.

Conclusions:

The Miller-Madow and jackknife estimators are asymptotically normal under the derived conditions.
This work provides a theoretical foundation for using these estimators in complex information systems.
The findings advance the understanding of entropy estimation on infinite alphabets.