Nonparametric density estimates consistent of the order of n <Superscript>−1/2</Superscript> in the L <Subscript>1</Subscript>–norm
We introduce an approximate minimum Kolmogorov distance density estimate [InlineMediaObject not available: see fulltext.] of a probability density f <Subscript>0</Subscript> 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 <Subscript>0</Subscript>. If this degree is finite then the approximate minimum Kolmogorov distance estimate is consistent of the order of n <Superscript>−1/2</Superscript> in the L <Subscript>1</Subscript>-norm and also in the expected L <Subscript>1</Subscript>-norm. Comparisons with two other criteria leading to the same order of consistency are given. Copyright Springer-Verlag 2004
Year of publication: |
2004
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---|---|
Authors: | Kůs, Václav |
Published in: |
Metrika. - Springer. - Vol. 60.2004, 1, p. 1-14
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Publisher: |
Springer |
Subject: | Kolmogorov distance | total variational distance | minimum distance density estimates | order of consistency |
Saved in:
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