A test for singularity

Attila Frigyesi; Ola Hössjer

doi:10.1016/S0167-7152(98)00087-X

A test for singularity

Attila Frigyesi, Ola Hössjer

Anesthesiology and Intensive Care

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Abstract

he LP-norm and other functionals of the kernel estimate of density functions las functions of the bandwidth) are studied as means to test singularity. Given an absolutely continuous distribution function, the LP-norm, and the other studied functionals, will converge under some mild side-constraints as the bandwidth decreases. In the singular case, the functionals will diverge. These properties may be used tc, test whether data comes from an arbitrarily large class of absolutely continuous distributions or not.

Original language	English
Pages (from-to)	215-226
Journal	Statistics and Probability Letters
Volume	40
Issue number	3
DOIs	https://doi.org/10.1016/S0167-7152(98)00087-X
Publication status	Published - 1998

Subject classification (UKÄ)

Probability Theory and Statistics

Free keywords

singularity
absolute continuity
Kernel density estimation

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10.1016/S0167-7152(98)00087-X

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title = "A test for singularity",

abstract = "he LP-norm and other functionals of the kernel estimate of density functions las functions of the bandwidth) are studied as means to test singularity. Given an absolutely continuous distribution function, the LP-norm, and the other studied functionals, will converge under some mild side-constraints as the bandwidth decreases. In the singular case, the functionals will diverge. These properties may be used tc, test whether data comes from an arbitrarily large class of absolutely continuous distributions or not.",

keywords = "singularity, absolute continuity, Kernel density estimation",

author = "Attila Frigyesi and Ola H{\"o}ssjer",

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journal = "Statistics and Probability Letters",

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T1 - A test for singularity

AU - Frigyesi, Attila

AU - Hössjer, Ola

PY - 1998

Y1 - 1998

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AB - he LP-norm and other functionals of the kernel estimate of density functions las functions of the bandwidth) are studied as means to test singularity. Given an absolutely continuous distribution function, the LP-norm, and the other studied functionals, will converge under some mild side-constraints as the bandwidth decreases. In the singular case, the functionals will diverge. These properties may be used tc, test whether data comes from an arbitrarily large class of absolutely continuous distributions or not.

KW - singularity

KW - absolute continuity

KW - Kernel density estimation

U2 - 10.1016/S0167-7152(98)00087-X

DO - 10.1016/S0167-7152(98)00087-X

M3 - Article

SN - 0167-7152

VL - 40

SP - 215

EP - 226

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 3

ER -

A test for singularity

Abstract

Subject classification (UKÄ)

Free keywords

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