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1、JunShaoMathematicalStatistics:ExercisesandSolutionsContentsPreface................................viiNotation...............................xiTerminology............................xvSomeDistributions........................xxiiiChapter1.ProbabilityTheory................1Chapter2.
2、FundamentalsofStatistics...........51Chapter3.UnbiasedEstimation...............95Chapter4.EstimationinParametricModels.......141Chapter5.EstimationinNonparametricModels....209Chapter6.HypothesisTests..................251Chapter7.ConfidenceSets..................309References........
3、......................351Index.................................353NotationR:Therealline.Rk:Thek-dimensionalEuclideanspace.c=(c,...,c):Avector(element)inRkwithjthcomponentc∈R;cis1kjconsideredasak×1matrix(columnvector)whenmatrixalgebraisinvolved.cτ:Thetransposeofavectorc∈Rkconsidere
4、dasa1×kmatrix(rowvector)whenmatrixalgebraisinvolved.c:TheEuclideannormofavectorc∈Rk,c2=cτc.
5、c
6、:Theabsolutevalueofc∈R.Aτ:ThetransposeofamatrixA.Det(A)or
7、A
8、:ThedeterminantofamatrixA.tr(A):ThetraceofamatrixA.A:ThenormofamatrixAdefinedasA2=tr(AτA).A−1:TheinverseofamatrixA.A−:Th
9、egeneralizedinverseofamatrixA.A1/2:ThesquarerootofanonnegativedefinitematrixAdefinedbyA1/2A1/2=A.A−1/2:TheinverseofA1/2.R(A):ThelinearspacegeneratedbyrowsofamatrixA.Ik:Thek×kidentitymatrix.Jk:Thek-dimensionalvectorof1’s.∅:Theemptyset.(a,b):Theopenintervalfromatob.[a,b]:Theclosedinte
10、rvalfromatob.(a,b]:Theintervalfromatobincludingbbutnota.[a,b):Theintervalfromatobincludingabutnotb.{a,b,c}:Thesetconsistingoftheelementsa,b,andc.A1×···×Ak:TheCartesianproductofsetsA1,...,Ak,A1×···×Ak={(a1,...,ak):a1∈A1,...,ak∈Ak}.xixiiNotationσ(C):Thesmallestσ-fieldthatcontainsC.σ(
11、X):Thesmallestσ-fieldwithrespecttowhichXismeasurable.ν1×···×νk:Theproductmeasureofν1,...,νkonσ(F1×···×Fk),whereνiisameasureonFi,i=1,...,k.B:TheBorelσ-fieldonR.Bk:TheBorelσ-fieldonRk.Ac:ThecomplementofasetA.A∪B:TheunionofsetsAandB.∪Ai:TheunionofsetsA1,A2,....A∩B:TheintersectionofsetsA
12、andB.∩Ai:TheintersectionofsetsA1,
