基于L (2) Wasserstein距离的正态性检验的Bootstrap方法.pdf

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应用概率统计第38卷ChineseJournalofAppliedProbabilityandStatistics
应用概率统计第38卷ChineseJournalofAppliedProbabilityandStatistics
第2期2022年4月Apr.,2022,,,-194
doi:.1001-
ABootstrapMethodofTestingNormalityBasedonL2
WassersteinDistance∗
YANGChaoran
(InformationDepartment,BeijingUniversityofTechnology,Beijing,100124,China)
CHANGGuangping⋆
(InstituteofFundamentalandInterdisciplinarySciences,BeijingUnionUniversity,
Beijing,100101,China)
Abstract:
mainlydefinedintwotypes:oneisempiricaldistributionfunctiontest,theotheriscorrelation
,weproposeanewtwo-steptestmethodbasedontheL2

thepropertiesofthenewtestmethodunderthenullhypothesis,andcomparethepowerwithother
,thenewmethodisappliedtoanalyse

identifyingasymmetriclong-tailedalternatives.
Keywords:normalitytest;L2Wassersteindistance;bootstrapmethod
2020MathematicsSubjectClassification:62F40
Citation:YANGCR,
Wassersteindistance[J].ChineseJApplProbabStatist,2022,38(2):179–194.
§
Instatisticaltheoryandapplication,manystatisticalmethodsoftenrequiredatatobe
normallydistributed,suchas:Ztest,ttest,χ2test,Ftest,varianceanalysis,correlation
analysis,parameterestimationandparameterhypothesistesting,,in
linearregressionanalysis,abasicassumptionisthattheresidualsarenormallydistributed;
inttest,thefirstthingistodeterminewhetherthesamplepopulationfollowsthenormal
distribution.
∗
TheprojectwassupportedbyBeijingUnionUniversityFoundation().
⋆Correspondingauthor,E-mail:******@.
ReceivedJune13,