eprintid: 20895
rev_number: 11
eprint_status: archive
userid: 2326
dir: disk0/00/02/08/95
datestamp: 2016-06-09 07:19:25
lastmod: 2016-06-27 09:12:02
status_changed: 2016-06-09 07:19:25
type: article
metadata_visibility: show
creators_name: Polonik, Wolfgang
title: Concentration and Goodness-of-Fit in Higher Dimensions: (Asymptotically) Distribution-Free Methods
subjects: ddc-510
divisions: i-110400
keywords: Diagnostic plots; empirical process theory; generalized quantile transformation; Kolmogoroff-Smirnov test; minimum volume sets
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.
date: 1999
publisher: IMS Business Office
id_scheme: DOI
id_number: 10.11588/heidok.00020895
schriftenreihe_cluster_id: sr-10a
schriftenreihe_order: 33
ppn_swb: 1657259781
own_urn: urn:nbn:de:bsz:16-heidok-208956
language: eng
bibsort: POLONIKWOLCONCENTRAT1999
full_text_status: public
publication: Annals of Statistics
volume: 27
number: 4
place_of_pub: Haward, Calif.
pagerange: 1210-1229
issn: 0090-5364
citation:   Polonik, Wolfgang  (1999) Concentration and Goodness-of-Fit in Higher Dimensions: (Asymptotically) Distribution-Free Methods.  Annals of Statistics, 27 (4).  pp. 1210-1229.  ISSN 0090-5364     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/20895/1/beitrag.33.pdf