多参数指数族参数经验贝叶斯估计的收敛速度

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1、COMUNICATIONSINSTATISTICS1996，25(6)，1325-1334CONVERGENCERATESFOREMPIRICALBAYESESTIMATORSOFPARAMETERSINLINEARREGRESSIONMODELSHengqingTongDepartmentofMathematicsandPhysicsWuhanUniversityofTechnologyWuhan,Hubei,430070,P.R.ChinaKeyWordsandPhrases:empiricalBayes；conve

2、rgencerate；jointestimation;inversestretchoperation;variancecomponentmodel.ABSTRACTInthispaper,theconvergenceratesoftheestimatorsoftheregressioncoefficientsandtheerrorvarianceinalinearmodelareobtained.Theratescanapproximatetoarbitrarily.Theconvergenceoftheestimato

3、rsoftheregressioncoefficientsandthevariancecomponentsinavariancecomponentmodelisalsoinvestigated.Theinvestigationmakesuseoftheresultsconcerningtheconvergenceratesoftheestimatorsoftheparametersinmulti-parameterexponentialfamilies.1.IntroductionWind(1972)investigat

4、edtheempiricalBayes()estimatorsoftheregressioncoefficientsinamultivariatelinearmodel.Ofcourse,atthattimetheconvergenceratecouldnotbegiven.Singh(1977,1979)obtainedtheratesofconvergenceoftheestimatorsinone-parameterexponentialfamilies.Tong(1996)studiedtheconvergenc

5、eratesoftheestimatorsofparametersinmulti-parameterexponentialfamilies.Nowweinvestigatetheconvergenceratesofthejointestimatorsoftheregressioncoefficientandtheerrorvarianceinalinearmodel,thenweinvestigatetheconvergenceoftheestimatorsoftheregressioncoefficientsandth

6、evariancecomponentsinavariancecomponentmodel.Letandbei.i.d.sampleswithdensity.anditspartialderivativesarelocallybounded.isthedimensionofanorthogonalpolynomialspaceinwhichthekernelestimatorsofthedensityareconstructed.Theparameterofhasapriordistribution.ItsBayesris

7、kandriskweredefinedbytheauthor(1995).Wehaveproved:THEOREMSuppose，and(1.1)(1.2)(1.3)Then(1.4)1.Convergenceofthekernelestimatorofdensityanditspartialderivativeinmulti-parameterexponentialfamiliesFirst，weconsideralinearmodelwithanomaldistribution:(2.1)Thecolumnsofth

8、edesignmatrixarefullrank.andareunknown.denotestheleastsquareestimationof.Theconditionaldensityofis(2.2)Where.Second,thedensity(2.2)istransformedintoamulti-para