Annals of the Institute of Statistical Mathematics
, Volume 32, Issue 1, pp 241245
First online:
Nonparametric estimation of Matusita's measure of affinity between absolutely continuous distributions
 Ibrahim A. AhmadAffiliated withMacMaster University
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LetF andG be two distribution functions defined on the same probability space which are absolutely continuous with respect to the Lebesgue measure with probability densitiesf andg, respectively. Matusita [3] defines a measure of the closeness, affinity, betweenF andG as:\(\rho = \rho (F,G) = \int {[f(x)g(x)]^{1/2} } dx\). Based on two independent samples fromF andG we propose to estimate ρ by\(\hat \rho = \int {[\hat f(x)\hat g(x)]^{1/2} } dx\), where\(\hat f(x)\) and\(\hat g(x)\) are taken to be the kernel estimates off(x) andg(x), respectively, as given by Parzen [5].
In this note sufficient conditions are given such that (i)\(E(\hat \rho  \rho )^2 \to 0\) asx→∞ and (ii)\(\hat \rho  \rho \) with probability one, asn→∞.
 Title
 Nonparametric estimation of Matusita's measure of affinity between absolutely continuous distributions
 Journal

Annals of the Institute of Statistical Mathematics
Volume 32, Issue 1 , pp 241245
 Cover Date
 198012
 DOI
 10.1007/BF02480328
 Print ISSN
 00203157
 Online ISSN
 15729052
 Publisher
 Kluwer Academic Publishers
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 Authors

 Ibrahim A. Ahmad ^{(1)}
 Author Affiliations

 1. MacMaster University, Canada