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Statistical analysis of the estimation of distance measures

✍ Scribed by Mark Pinsky; Dina Yogev-Einot; David Avnir

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 133 KB
Volume: 24
Category: Article
ISSN: 0192-8651
DOI: 10.1002/jcc.10202

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✦ Synopsis

Abstract

Distance functions serve for quantitative evaluation of the degree of similarity, shape content, symmetry, chirality, and so on. We have developed a general methodology and a general computational tool for the estimation of the value of the distance function and of the error in that estimation, which originates in the experimental uncertainty in the location of the set of points of the studied structure (such as that expressed by the atomic displacement factor in X‐ray data analysis). © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 786–796, 2003

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## Abstract Let μ be a Radon measure with compact support in IR^n^ such that equation image We show that the imw of μ x μ under the distance map (x, y) → |x‐ y| is an absolutely continuous measure with density of class C^a^‐(n+1)/2. As a corollary we get that If AC IR^n^ is a Suslin set with Haus