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• W3132544841 abstract "We revisit the problem of the estimation of the differential entropy $H(f)$ of a random vector $X$ in $R^d$ with density $f$, assuming that $H(f)$ exists and is finite. In this note, we study the consistency of the popular nearest neighbor estimate $H_n$ of Kozachenko and Leonenko. Without any smoothness condition we show that the estimate is consistent ($E{|H_n - H(f)|} to 0$ as $n to infty$) if and only if $mathbb{E} { log ( | X | + 1 )} < infty$. Furthermore, if $X$ has compact support, then $H_n to H(f)$ almost surely." @default.
• W3132544841 created "2021-03-01" @default.
• W3132544841 creator A5032807145 @default.
• W3132544841 creator A5070394029 @default.
• W3132544841 date "2021-02-25" @default.
• W3132544841 modified "2023-10-01" @default.
• W3132544841 title "On the consistency of the Kozachenko-Leonenko entropy estimate" @default.
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• W3132544841 hasPublicationYear "2021" @default.
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