财务危机预警模式之再探讨-应用支撑向量机及逻辑斯回归

2004May22,[e-mail][e-mail]yPredictionModelwithSupportVectorMachineandLogisticRegressionAbstractThispaperexaminesthreeissues-choice-basedsamplebias,predictorselecting,andconsistency-inbankruptcyprediction.SupportVectorMachineandLogisticregressionareusedtopredictbankruptcy.TheselectedtechniquesareAltmananalysisandforwardWaldselectionmethod.Inempiricaltestthemostimportantdeterminantsofbankruptcyareleverageratioandoperatingprofitratio.ThepredictionresultswereachievedusingSupportVectorMachineandforwardWaldselectionmethod.Thechoice-basedsamplebiasisstatisticallysignificant.Thepredictresultsdoesn’tdecreasingfollowingtimepassing.Keywords:Bankruptcy;Choice-BasedSampleBias;SupportVectorMachines;Logisticregression2004-50-30Beaver(1966)(DischotomousClassificationTest)Z-score(Altman,1968)AltmanMultipleDiscriminantanalysisOhlson,1980Logisticanalysis(Ohlson,1980)Probitanalysis1990Altman,MarcoandVaretto,1994Choice-BasedSampleBias(paired-sample)Beaver,1966;Altman,1968;JoandHan,1996Zmijewski,1984PlattandPlatt,2002(Random)Beaver,1966;Altman,1968;Ohlson,1980;Zmijewski,1984;Altmanetal,1994;PlattandPlatt,2002Altman,1968;Ohlson,1980;Zmjiewski,1984;Altmanetal.,1994;Lennox,1999;PlattandPlatt,2002(Geneticalgorithm)Backetal.,1996Altmanetal.,1994VanGesteletal2003Support-51-VectorMachineApproach,SVMSVMLogitBeaver(1966)(dischotomousclassificationTest)Altman(1968)(discriminantanalysis)1946-1965Z-scoreZ-score1.81(logisticregressionmodel)1980Ohlson(1980)1980(JoandHan,1996;Altman,MarcoandVaretto,1994)VanGesteletal2003SupportVectorMachineApproach,SVMSupportVectorMachineApproach,SVMLogistic3-12004-52-Plattetal.,1990Plattetal.1990Altman196822Altman225Z-score(Ft)5Altman(Backetal.,1996)87923868838991SupportVectorMachineApproach,SVMLogit495050-187927267Beaver,1966;Altman,1968;Altmanetal.,1994;Backetal.,1996-53-111246810Dimitras,etal.,199618Plattetal.(2002)Financialleverage3-13-1S11./%S22.(++)/%L11./%L22./%L33./%L44.(+)/%L55./%P11.()/%P22.()/%P33.(+*(1-))/%P44./%T11./T22./T33./T44./T55./C11./%C22.(-)/+++)%2004-54-tMann-WhitneyUlogisticPearsonSpearmanSupportVectorMachine,SVMSVMCoterandVapnik(1995)(Boundofthemisclassificationrisk)}{Niiidx1),(=ixidid1+=id1−=id3-10=+bxwT3-1xwb3-20≥+bxwTfor1+=id3-2bxwT+0for1−=id(discriminantfunction)3-300)(bxwxgT+=3-3x3-400wwrxxp+=3-4}{Niiidx1),(=wb3-5-55-1)(≥+bxwdiTifori=1,2,,N(3-5)(=Φ3-6iiTibxwdξ−≥+1)(fori=1,2,,N(3-6iξ(slackvariables)3-6∑==ΦNii1)(ξξwiξ3-7∑=+=ΦNiiTC),(ξξ3-7trade-offregularizationparameteruser-specifiedLagrange(Lagrangemultipliers)dualproblem{}Niiidx1),(=Lagrange{}Nii1=αjTijijNiNiNjiixxddQαααα∑∑∑===−=11121)(3-8subjectto(a)01=∑=iNiidα(b)Ci≤≤α0fori=1,2,…,N),(jixxKinner-productkerneljTixx2004-56-{}NjijixxKK1),(),(==),(21)(111jijijNiNiNjiixxKddQαααα∑∑∑===−=3-9K(x,xi)Mercer’sMercer’stheorem1.PolynomiallearningmachinepiTxx)1(+2.Radial-basisfunction)21exp(22ixx−−σ3.Two-layerperceptron)tanh(10ββ+iTxxLogisticlogistic2ipjjjippXXXXYεβαεβββα++=+++++=∑=12211...Yi=1Yi=0jjiXXXβββαε−−−−−=...12211Yi=1jjiXXXβββαε−−−−−=...2211Yi=0iε1iiiXYEπ=)(P(Yi=1)iπXiXiiπ1,Xiiπ0iπXiS)...()...(11111)(jjjjXXXXxββαββαπ+++++++=λλ10≤≤iπεπ+=)(xY-57-)exp()1/(1∑=+=−pjjjXβαππjpjjX∑=+=−1)1log(βαππ3-103-10logistictransformlogisticlog()1ππ−logoddsratioπ=P(Y=1)(1-π)=P(Y=0)ππ−12oddsratiologisticMaximumlikelihoodEstimation,MLEαiβlogisticWald2ˆ)/ˆ(kSEWkββ=kSEβˆkβˆ0:0=kHβWald4-1888990911.21.887922004-58-4-1(a)(b)(a/b)878622111184371.83%88871212222131174621.73%89881151111115311.51%90891253112155841.37%919071212136381.25%92912113186691.20%111531291121032847233210.24%4-21.4-59-4-2(N=64)(N=64)(N=3158)MeanStd.DeviationMeanStd.DeviationMeanStd.DeviationS10.6341640.8719731.3185490.9668751.36011591.1501107S20.5076661.2269181.4217391.536991.55477652.4766053L11.4493420.5870740.9896490.3630560.9751810.3871781L22.060976.7883221.0095570.2747091.02915480.2742057L33.2140084.4342531.0948680.635931.17849661.1600884L40.8944190.9140024.39066623.5989011.98482586.3779446L51.99449319.9439748.799737510.716231130.1111441740.953287P123.7002693.3573542.89046813.4351321.45659028.869226P2-6.03510951.7456391.3104763.9138461.17494216.6974429P3-60.312427366.3017776.024078102.0629690.284020315.6641903P45.29508478.4273061.2002615.0081723.4352256228.6809184T13.0075789.2381231.2799960.876391.39544220.9011264T2-1.56667230.821552.71227.9919491.61390765.7345161T3-597.9125525657.2971921.3795611.4187224.115847592.834866T41.2602981.6839385.83564132.3785673.473532113.0487216T5-9.34746124.041011.29270.8932611.53642971.4419082C1-1.33364816.3707824.71054420.7071682.748625328.027306C2-21.059371437.561882-0.31870116.7442050.851216425.14040512004-60-4-3One-SampleKolmogorov-SmirnovTest4-4Mann-WanneyUTestKolmogorov-SmirnovZSig.ZSig.S12.6790**S1-7.4290**S22.4290**S2-6.5880**L10.9380.343L1-5.4930**L25.1660**L2-5.5960**L33.0750**L3-5.5690**L44.9760**L4-4.4570**L54.9610**L5-2.890.004**P14.0730**P1-1.3460.178P23.6120**P2-2.0760.038*P35.1720**P3-2.5650.01**P43.6990**P4-2.2320.026*T14.3520**T1-1.6290.103T25.6090**T2-0.10