asymptotic theory of a test for the constancy of regression coefficients against

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1、AsymptoticTheoryofaTestfortheConstancyofRegressionCoefficientsAgainsttheRandomWalkAlternativeAuthor(s):SeijiNabeyaandKatsutoTanakaReviewedwork(s):Source:TheAnnalsofStatistics,Vol.16,No.1(Mar.,1988),pp.218-235Publishedby:InstituteofMathematicalStatistic

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5、No.1,218-235ASYMPTOTICTHEORYOFATESTFORTHECONSTANCYOFREGRESSIONCOEFFICIENTSAGAINSTTHERANDOMWALKALTERNATIVEBYSEIJINABEYAANDKATSUTOTANAKAHitotsubashiUniversityTheLBI(locallybestinvariant)testissuggestedundernormalityfortheconstancyofregressioncoefficients

6、againstthealtemativehypothesisthatonecomponentofthecoefficientsfollowsarandomwalkprocess.Wediscussthelimitingnullbehavioroftheteststatisticwithoutassumingnormalityundertwosituations,wheretheinitialvalueoftherandomwalkprocessisknownorunknown.Thelimiting

7、distributionisthatofaquadraticfunc-tionalofBrownianmotionandthecharacteristicfunctionisobtainedfromtheFredhohmdeterminantassociatedwithacertainintegralequation.Thelimitingdistributionisthencomputedbynumericalinversionofthechar-acteristicfunction.1.Intr

8、oduction.InthispaperweareconcernedwiththemodelYt=XtIt+ZtY+et,Pt=Pt-,+ut,t=1,2,....where(i){fytisasequenceofscalarobservations,whereas{xt}and{zt}arescalarandpx1nonstochastic,fixedsequences,respectively;(ii){et}and{ut}areindependentofeach