Nonparametric density estimates consistent of the order of n −1/2 in the L 1 –norm

Václav Kůs

Metrika: International Journal for Theoretical and Applied Statistics, 2004, vol. 60, issue 1, 14 pages

Abstract: We introduce an approximate minimum Kolmogorov distance density estimate [InlineMediaObject not available: see fulltext.] of a probability density f 0 on the real line and study its rate of consistency for n→∞. We define a degree of variations of a nonparametric family [InlineMediaObject not available: see fulltext.] of densities containing the unknown f 0 . If this degree is finite then the approximate minimum Kolmogorov distance estimate is consistent of the order of n −1/2 in the L 1 -norm and also in the expected L 1 -norm. Comparisons with two other criteria leading to the same order of consistency are given. Copyright Springer-Verlag 2004

Keywords: Kolmogorov distance; total variational distance; minimum distance density estimates; order of consistency (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:60:y:2004:i:1:p:1-14

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DOI: 10.1007/s001840300286

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