The majorization relation express the fact that a given vector y is “more dissimilar” to a vector of constants than another vector x. An extended version of this relation can be applied to random variables X and Y with equal means and can be interpreted by saying that Y is “more variable than” X. In this paper we show that the majorization ordering (in a sort of weighted version) may used to define a relative dissimilarity ordering between distributions: if a distribution FX is smaller than a distribution FY relative to this ordering, then FX is closer to a given reference distribution F than FY. Applications of this ordering are given to the problem of nonparametric density estimation.

(2014). A relative dissimilarity ordering in the space of distribution functions, with statistical applications [conference presentation - intervento a convegno]. Retrieved from http://hdl.handle.net/10446/31171

A relative dissimilarity ordering in the space of distribution functions, with statistical applications

BERTOLI BARSOTTI, Lucio;LANDO, Tommaso
2014-01-01

Abstract

The majorization relation express the fact that a given vector y is “more dissimilar” to a vector of constants than another vector x. An extended version of this relation can be applied to random variables X and Y with equal means and can be interpreted by saying that Y is “more variable than” X. In this paper we show that the majorization ordering (in a sort of weighted version) may used to define a relative dissimilarity ordering between distributions: if a distribution FX is smaller than a distribution FY relative to this ordering, then FX is closer to a given reference distribution F than FY. Applications of this ordering are given to the problem of nonparametric density estimation.
2014
BERTOLI BARSOTTI, Lucio; Lando, Tommaso
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/31171
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