mycoreobjectrosdok_document_0000027967rosdok_document_0000027967rosdokdocumentrosdok_derivate_00002299062026-10-14T11:22:28.495Z2026-10-14T10:00:22.149ZeditorKEeditorKEpublished1rosdok_derivate_0000229906truetruederivate_types:fulltextVolltextfulltextwf_edit_epub wf_register_epubstate:publishedstate:publishedveröffentlichtpublishedrosdok_id00005830198673045XOau2026-10-142026-10-14T10:10:28ZrdaConverted from PICA to MODS using Pica2MODS XSLT Transformer 2.14-SNAPSHOT [SCM: "" "" ""] with mode 'DEFAULT'.WorkingpaperRandomized goodness of fit testsGoodness of fi…t tests based on the empirical distribution function fail to be asymptotically distribution free if parameters are estimated. Asymptotically, the empirical process with estimated parameters is a centered Gaussian process with a covariance that di¤ers from the covariance function of the Brownian bridge. If the maximum likelihood estimator is used then the new covariance function is smaller, in the Loewner semiorder, than the covariance function of the Brownian bridge. Therefore one may transform the empirical process with estimated parameters back to a Brownian bridge by adding an independent process that is suitably constructed. Classical goodness of …t statistics have aftzer this transformation an asymptotic distribution as in the case of known parameters. The power under local alternatives of this new goodness of fit tests is studied and computer simulations compare the new test with their bootstrap versions.FriedrichLiese1944 - 2018VerfasserInaut140883363BingLiu1981 -VerfasserInaut102958561Xhttps://purl.uni-rostock.de/rosdok/id00005830urn:nbn:de:gbv:28-rosdok_id00005830-110.18453/rosdok_id00005830510 MathematikMathematisch-Naturwissenschaftliche Fakultätalle Rechte vorbehaltenRechteinhaber Universität Rostockfrei zugänglich (Open Access)Lizenz Metadaten: CC0en1 Online-Ressource (28 Seiten)2009University of Rostock, Institute of MathematicsRostockmonographic20092026Universitätsbibliothek RostockRostock2026Universitätsbibliothek Rostockhttps://purl.uni-rostock.de/rosdok/id00005830F. Liese and B. Liurosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-809/10009-0001doctype:epubdoctype:epubDokumenttypDocument typedoctype:epub.workingpaperdoctype:epub.workingpaperWorkingpaperworking paperdiniPublType:workingPaper diniPublType2022:WorkingPaperinfo:eu-repo/semantics/workingPaperdocumentdiniPublType2022:WorkingPaperdiniPublType2022:WorkingPaperArbeitspapierWorking paperKDSF (Pu37)SDNB:510SDNB:510510 Mathematik510 Mathematicsinstitution:unirostockinstitution:unirostockUniversität RostockUniversity of RostockUniversität RostockUniversität RostockUni.Rostockhttp://d-nb.info/gnd/38329-6institution:unirostock.mnfinstitution:unirostock.mnfMathematisch-Naturwissenschaftliche FakultätFaculty of Mathematics and Natural SciencesUniversität Rostock. Mathematisch-Naturwissenschaftliche FakultätMathematisch-Natur-<br />wissenschaftliche FakultätUni.Rostock.Fakultaet.MNFhttp://d-nb.info/gnd/2147083-2licenseinfo:worklicenseinfo:workWerkworklicenseinfo:work.rightsreservedlicenseinfo:work.rightsreservedalle Rechte vorbehaltenall rights reserved/creativecommons/r/reserved/0.9/88x31.png[DE-28]Urheberrechtsschutz 1.0$gRights Statements$uhttp://rightsstatements.org/vocab/InC/1.0/http://rightsstatements.org/vocab/InC/1.0/http://rightsstatements.org/vocab/InC/1.0/licenseinfo:depositlicenseinfo:depositVeröffentlichungsgenehmigungpermission to storelicenseinfo:deposit.rightsunirostocklicenseinfo:deposit.rightsunirostockRechteinhaber Universität Rostockrightsholder Rostock Universityaccesscondition:openaccessaccesscondition:openaccessfrei zugänglich (Open Access)open accesshttp://purl.org/coar/access_right/c_abf2OAfreeinfo:eu-repo/semantics/openAccess[DE-28]Open Access$gControlled Vocabulary for Access Rights$uhttp://purl.org/coar/access_right/c_abf2licenseinfo:metadatalicenseinfo:metadataLizenzen für Metadatenlicenseinfo:metadata.cc0licenseinfo:metadata.cc0Lizenz Metadaten: CC0license metadata: CC0/creativecommons/p/zero/1.0/88x31.pnghttps://creativecommons.org/publicdomain/zero/1.0/rfc5646:enrfc5646:enEnglischEnglishengengRandomized goodness of fit testsRandomized goodness of fit testsgnd:140883363gnd:102958561Xgnd:140883363gnd:102958561Xrosdok_document_0000027967-d3751838e49gnd:140883363Friedrich LieseFriedrich Lieserosdok_document_0000027967-d3751838e63gnd:102958561XBing LiuBing LiuFriedrich LieseBing LiuFriedrich LieseBing LiuFriedrich LieseBing LiuRostockUniversity of Rostock, Institute of Mathematicsepub.workingpaperhttps://purl.uni-rostock.de/rosdok/id00005830urn:nbn:de:gbv:28-rosdok_id00005830-110.18453/rosdok_id00005830Goodness of fi…t tests based on the empirical distribution function fail to be asymptotically distribution free if parameters are estimated. Asymptotically, the empirical process with estimated parameters is a centered Gaussian process with a covariance that di¤ers from the covariance function of the Brownian bridge. If the maximum likelihood estimator is used then the new covariance function is smaller, in the Loewner semiorder, than the covariance function of the Brownian bridge. Therefore one may transform the empirical process with estimated parameters back to a Brownian bridge by adding an independent process that is suitably constructed. Classical goodness of …t statistics have aftzer this transformation an asymptotic distribution as in the case of known parameters. The power under local alternatives of this new goodness of fit tests is studied and computer simulations compare the new test with their bootstrap versions.20092009Preprints aus dem Institut für Mathematikrosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-809/10009-0001https://purl.uni-rostock.de/rosdok/id000058163255797-8F. Liese and B. Liuepub.workingpaper1 Liese_randomized_2009.pdf 9949325 b6253998175f9301f9f02c1e4e03ce05 rosdok_id00005830198673045XOau2026-10-142026-10-14T10:10:28ZrdaConverted from PICA to MODS using Pica2MODS XSLT Transformer 2.14-SNAPSHOT [SCM: "" "" ""] with mode 'DEFAULT'.WorkingpaperRandomized goodness of fit testsGoodness of fi…t tests based on the empirical distribution function fail to be asymptotically distribution free if parameters are estimated. Asymptotically, the empirical process with estimated parameters is a centered Gaussian process with a covariance that di¤ers from the covariance function of the Brownian bridge. If the maximum likelihood estimator is used then the new covariance function is smaller, in the Loewner semiorder, than the covariance function of the Brownian bridge. Therefore one may transform the empirical process with estimated parameters back to a Brownian bridge by adding an independent process that is suitably constructed. Classical goodness of …t statistics have aftzer this transformation an asymptotic distribution as in the case of known parameters. The power under local alternatives of this new goodness of fit tests is studied and computer simulations compare the new test with their bootstrap versions.FriedrichLiese1944 - 2018VerfasserInaut140883363BingLiu1981 -VerfasserInaut102958561Xhttps://purl.uni-rostock.de/rosdok/id00005830urn:nbn:de:gbv:28-rosdok_id00005830-110.18453/rosdok_id00005830510 MathematikMathematisch-Naturwissenschaftliche Fakultätalle Rechte vorbehaltenRechteinhaber Universität Rostockfrei zugänglich (Open Access)Lizenz Metadaten: CC0en1 Online-Ressource (28 Seiten)2009University of Rostock, Institute of MathematicsRostockmonographic20092026Universitätsbibliothek RostockRostock2026Universitätsbibliothek Rostockhttps://purl.uni-rostock.de/rosdok/id00005830F. Liese and B. Liurosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-809/10009-0001 2026-10-14T10:00:22.149Z 2026-10-14T11:22:28.495Z 2026-10-24T11:22:28.505Z editorKE {"identifier":"rosdok/id00005830","type":"local_id","additional":"","service":"MCRLocalID","created":"2026-10-14T10:00:22.160Z"} {"identifier":"urn:nbn:de:gbv:28-rosdok_id00005830-1","type":"dnbUrn","additional":"","service":"RosDokURN","created":"2026-10-14T10:00:22.170Z"} {"identifier":"https://purl.uni-rostock.de/rosdok/id00005830","type":"purl","additional":"","service":"RosDokPURL","created":"2026-10-14T10:00:22.175Z","registrationStarted":"2026-10-14T10:10:57.843Z"} {"identifier":"10.18453/rosdok_id00005830","type":"doi","additional":"","service":"RosDokDOI","created":"2026-10-14T10:00:22.180Z","registrationStarted":"2026-10-14T10:10:57.627Z","registered":"2026-10-14T10:10:59.165Z"} editorKEfulltextfile/rosdok_document_0000027967/rosdok_derivate_0000229906/Liese_randomized_2009.pdfRandomized goodness of fit testsRandomized goodness of fit testsgnd:140883363gnd:102958561Xgnd:140883363gnd:102958561Xrosdok_document_0000027967-d3751838e49gnd:140883363Friedrich LieseFriedrich Lieserosdok_document_0000027967-d3751838e63gnd:102958561XBing LiuBing LiuFriedrich LieseBing LiuFriedrich LieseBing LiuFriedrich LieseBing LiuRostockUniversity of Rostock, Institute of Mathematicsepub.workingpaperhttps://purl.uni-rostock.de/rosdok/id00005830urn:nbn:de:gbv:28-rosdok_id00005830-110.18453/rosdok_id00005830Goodness of fi…t tests based on the empirical distribution function fail to be asymptotically distribution free if parameters are estimated. Asymptotically, the empirical process with estimated parameters is a centered Gaussian process with a covariance that di¤ers from the covariance function of the Brownian bridge. If the maximum likelihood estimator is used then the new covariance function is smaller, in the Loewner semiorder, than the covariance function of the Brownian bridge. Therefore one may transform the empirical process with estimated parameters back to a Brownian bridge by adding an independent process that is suitably constructed. Classical goodness of …t statistics have aftzer this transformation an asymptotic distribution as in the case of known parameters. The power under local alternatives of this new goodness of fit tests is studied and computer simulations compare the new test with their bootstrap versions.20092009Preprints aus dem Institut für Mathematikrosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-809/10009-0001https://purl.uni-rostock.de/rosdok/id000058163255797-8F. Liese and B. Liu[xslt]Saxonrosdok_id00005830https://purl.uni-rostock.de/rosdok/id00005830198673045X10.18453/rosdok_id00005830urn:nbn:de:gbv:28-rosdok_id00005830-1Friedrich Liese, Bing LiuLiese Friedrich, Liu BingRandomized goodness of fit testsWorkingpaperworking paperUniversity of Rostock, Institute of Mathematics, 2009Goodness of fi…t tests based on the empirical distribution function fail to be asymptotically distribution free if parameters are estimated. Asymptotically, the empirical process with estimated parameters is a centered Gaussian process with a covariance that di¤ers from the covariance function of…rosdok_id000058160009-000109/1Friedrich LieseBing LiuRandomized goodness of fit testsPreprints aus dem Institut für MathematikUniversitätsbibliothek Rostockhttps://purl.uni-rostock.de/rosdok/id00005830FriedrichLiese1944 - 2018VerfasserInaut140883363BingLiu1981 -VerfasserInaut102958561X[purl]https://purl.uni-rostock.de/rosdok/id00005830[urn]urn:nbn:de:gbv:28-rosdok_id00005830-1[doi]10.18453/rosdok_id00005830open_access20092009epoch:21th_centuryrfc5646:endoctype:epub.workingpaperaccesscondition:openaccessSDNB:510institution:unirostock.mnfstate:published