ON THE ASYMPTOTIC EQUIVALENCE OF HELLINGER DISTANCE AND KULLBACK-LEIBLER LOSS

Yuichiro Kanazawa; Atsuyuki Kogure; Sang-Gil Lee

doi:10.14490/jjss1995.29.1

Yuichiro Kanazawa, Atsuyuki Kogure, Sang-Gil Lee

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Keywords: Akaike's Information criterion, Hellinger distance, histogram, integrated absolute error, integrated square error, kernel estimator, Kullback-Leibler loss, least-squares cross-validation, likelihood cross-validation

JOURNAL FREE ACCESS

1999 Volume 29 Issue 1 Pages 1-21

DOI https://doi.org/10.14490/jjss1995.29.1

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Abstract

Hellinger distance, Kullback-Leibler loss, and variance-stabilizing integrated square error are shown to be asymptotically equivalent up to a constant. Simulation confirmed the result. Implications of the result for dernel and histogram density estimation and the connection of the result with goodness of fit tests are discussed.

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