Measuring the Discrimination Quality of

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1、MeasuringtheDiscriminationQualityofSuitesofScorecards:ROCsGinis,BoundsandSegmentationLynCThomasQuantitativeFinancialRiskManagementCentre,UniversityofSouthamptonUKCSCCX,EdinburghAugust200711Outline•Howtomeasurescorecards–Measuresofdiscrimination•Divergence–expectationsofwoefuncti

2、ons•KolmogorvSmirnov-differenceindistributionfunction•ROCcurves-comparisonofdistributionfunction/businessmeasures•Ginicoefficient/Dconcordancestatistic-–SimpleboundforROCCurve–Relationshipbetweenmeasuresofdiscrimination•Segmentingandmeasuresofsegmentation–Whysegmentandbuilddiffe

3、rentscorecardsoneachsegment–Howmuchofdiscriminationduetosegmentationandhowmuchtoscorecard?–Someexamplesfrombehaviouralscorecards22Measuringscorecardsincreditscoring•Threedifferentaspectsofascorecardsperformancethatonemightwanttomeasure•Discriminatorypower(onlyusesscorecard)–Howg

4、oodisthesystematseparatingthetwoclassesofgoodsandbads•Divergencestatistic•Mahalanobisdistance•Somer’sD-concordancestatistic•Kolmogorov–Smirnovstatistic•ROCcurve•Ginicoefficient•Calibrationofprobabilityforecast(usesscorecardandpopulationodds)–NotusedmuchuntilBaselrequirementsands

5、ofewtests•Chi-square(Hosmer-Lemeshow)test•BinomialandNormaltests•Categoricalpredictionerror(usesscorecard,populationoddsandcut-offscore)–Thisrequiresthescorecardandthecut-offscoresoonecanimplementthedecisionsandseehowmanyerroneousclassificationsthereareErrorrates2by2tablesandswa

6、psetsHypothesistests33Divergence•IntroducedbyKullbeck•ContinuousversionofInformationValue•Letf(s

7、G)(f(s

8、B))bedensityfunctionsofscoresofgoods,(G)(bads(B))inascorecard.DivergenceisthendefinedbyfsG(

9、)DivergenceD==∫(fsG(

10、)-fsB(

11、)logds=∫(fsG(

12、)-fsBwsds(

13、)()fsB(

14、)wherew(s)isthew

15、eightsofevidenceatscore.LikeExp(weightsofevidence)-Exp(weightsofevidence)goodsdistbaddist•D≥0andD=0Ûf(s

16、G)=f(s

17、B)•D®¥Ûnooverlapbetweenscoresofgoodsandbads•Reallycanonlycalculatethedivergencebysplittingscoresintobands.Ifibandswith∑gi=nGand∑bi=nBiIÎiIÎgn/gnInformationValueIV==

18、gn/-bn/lniG=gn/-bn/lniB∑(iGiB)∑(iGiB)44iIÎ