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1、18.443.StatisticsforApplications.byDmitryPanchenkoDepartmentofMathematicsMassachusettsInstituteofTechnologyContents1Estimationtheory.11.1Introduction................................1232.1Someprobabilitydistributions......................3383.1Methodofmoments............................84134.1Maximum
2、likelihoodestimators......................145175.1ConsistencyofMLE............................175.2AsymptoticnormalityofMLE.Fisherinformation...........206246.1Rao-Cr′amerinequality...........................257287.1E?cientestimators.............................298328.1Gammadistribution.............
3、...............328.2Betadistribution..............................339359.1Priorandposteriordistributions.....................35103810.1Bayesestimators..............................3810.2Conjugatepriordistributions.......................39ii114211.1Su?cientstatistic.............................421245
4、12.1Jointlysu?cientstatistics.........................4612.2Improvingestimatorsusingsu?cientstatistics.Rao-Blackwelltheorem.47134913.1Minimaljointlysu?cientstatistics....................4913.2α2distribution...............................51145314.1Estimatesofparametersofnormaldistribution............
5、.53155615.1Orthogonaltransformationofstandardnormalsample.........56166016.1FisherandStudentdistributions.....................60176317.1Con?denceintervalsforparametersofnormaldistribution.......6318Testinghypotheses.6718.1Testingsimplehypotheses.........................6718.2Bayesdecisionrules......
6、......................69197119.1Mostpowerfultestfortwosimplehypotheses..............73207620.1Randomizedmostpowerfultest......................7620.2Compositehypotheses.Uniformlymostpowerfultest..........79218121.1Monotonelikelihoodratio.........................8121.2Onesidedhypotheses...............
7、............82228622.1Onesidedhypothesescontinued......................86iii238923.1Pearson’stheorem.............................89249424.1Goodness-of-?ttest............................9424.2Goodness-
