Statistics for Applications（MIT） (1)

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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...........................257287.1Efficientestimators.............................298328.1Gammadistribution.............

3、...............328.2Betadistribution..............................339359.1Priorandposteriordistributions.....................35103810.1Bayesestimators..............................3810.2Conjugatepriordistributions.......................39ii114211.1Sufficientstatistic.............................421245

4、12.1Jointlysufficientstatistics.........................4612.2Improvingestimatorsusingsufficientstatistics.Rao-Blackwelltheorem.47134913.1Minimaljointlysufficientstatistics....................4913.2α2distribution...............................51145314.1Estimatesofparametersofnormaldistribution............

5、.53155615.1Orthogonaltransformationofstandardnormalsample.........56166016.1FisherandStudentdistributions.....................60176317.1Confidenceintervalsforparametersofnormaldistribution.......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-fittest............................9424.2Goodness-