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Concentration and Goodness-of-Fit in Higher Dimensions: (Asymptotically) Distribution-Free Methods

Polonik, Wolfgang

In: Annals of Statistics, 27 (1999), Nr. 4. pp. 1210-1229. ISSN 0090-5364

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Abstract

A novel approach for constructing goodness-of-fit techniquesin arbitrary (finite) dimensions is presented. Testing problems are considered as well as the construction of diagnostic plots. The approach is based on some new notion of massconcentration, and in fact, our basic testing problems are fomulatedas problems for " goodness-of-concentration ". It is this connection to concentration of measure that makes the approach conceptually simple.The presented test statistics are continuous functionals of certain processes which behave like the standard one-dimensional uniform empirical process.Hence, the test statistics behave like classical test statistics for goodness-of-fit. In particular, for single hypotheses they are asymptotically distribution free with well known asymptotic distribution. The simple technical idea behind the approach may be called a generalizedquantile transformation, where the role of one-dimensional quantiles in classicalsituations is taken over by so-called minimum volume sets.

Item Type: Article
Journal or Publication Title: Annals of Statistics
Volume: 27
Number: 4
Publisher: IMS Business Office
Place of Publication: Haward, Calif.
Date Deposited: 09 Jun 2016 07:19
Date: 1999
ISSN: 0090-5364
Page Range: pp. 1210-1229
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Uncontrolled Keywords: Diagnostic plots; empirical process theory; generalized quantile transformation; Kolmogoroff-Smirnov test; minimum volume sets
Schriftenreihe ID: Beiträge zur Statistik > Beiträge
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