廣義線性模型發(fā)展與應(yīng)用

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1、第十二屆中國精算年會The12thChinaActuarialAnnualConference廣義線性模型：發(fā)展與應(yīng)用孟生旺中國人民大學(xué)統(tǒng)計學(xué)院Email：mengshw@sina.com主要內(nèi)容?基本的廣義線性模型：理論與應(yīng)用–模型評價–費率約束?廣義線性模型的推廣與應(yīng)用–分布假設(shè)的推廣–GAM與GAMLSS（GAMforLocation,ScaleandShape)–神經(jīng)網(wǎng)絡(luò)與回歸樹?應(yīng)用案例2基本GLM：理論與應(yīng)用?分布假設(shè)：–正態(tài)–泊松、負二項：索賠頻率–伽馬、逆高斯：索賠強度–Tweedie：純保費–二項：續(xù)保率?連接函數(shù)：–恒等：加法模型–對數(shù)：乘法模型

2、，預(yù)測值大于零–logit：預(yù)測值在（0，1）區(qū)間3?Tweedie、泊松和伽馬的比較：p–Tweedie：V()???，1

3、離的加權(quán)和。Dwdy(,)iiiid(1，?)的圖示?模型評價2：殘差–Pearson殘差–Anscobe殘差rsign(y)d–Deviance殘差：Di–若分布假設(shè)是合理的，標準化處理后近似服從標準正態(tài)分布（下頁圖示）。–若偏差di的絕對值大于1，說明對這個觀察值的擬合效果較差。78rDrSD?(1h)iTT()(XWX)()()ii()Cookip?模型評價3：Type1和Type3分析LRStatisticsForType1Analysis2*LogSourceLikelihoodDFChi-SqPr>Chi-SqIntercept-1456.5376Own

4、erAge-1438.7844717.750.0131Model-1370.3694368.41<.0001CarAge-1247.84603122.52<.0001LRStatisticsForType3AnalysisSourceDFChi-SqPr>Chi-SqOwnerAge752.81<.0001Model3100.54<.0001CarAge3122.52<.000110?模型評價4：標準誤、置信區(qū)間和p值A(chǔ)nalysisOfMaximumLikelihoodParameterEstimatesStandardWald95%ConfidenceWaldC

5、hi-Pr>ChisParameterDFEstimateErrorLimitsSquareqIntercept15.13380.06375.00905.25866499.85<.0001OwnerAge17-2010.22630.11070.00940.44334.180.0409OwnerAge21-2410.22870.05980.11150.345914.630.0001OwnerAge25-2910.16420.04380.07830.250214.040.0002OwnerAge30-3410.11430.04200.03210.19667.430.00

6、64OwnerAge35-391-0.08770.0411-0.1684-0.00714.540.0330OwnerAge40-491-0.01290.0358-0.08310.05740.130.7197OwnerAge50-5910.00690.0372-0.06610.07990.030.8536OwnerAge60+00.00000.00000.00000.0000..CarAge0-310.69900.05160.59780.8002183.32<.0001CarAge4-710.61300.05160.51190.7141141.33<.0001CarA

7、ge8-910.35580.05980.23860.473035.43<.0001CarAgez10+00.00000.00000.00000.0000..Scale10.98520.12340.77071.259411?模型評價5：把樣本數(shù)據(jù)分為三組（數(shù)據(jù)充足）?訓(xùn)練樣本（trainingdata）?測試樣本(testdata)?評價樣本(validationdata)?模型評價6：Box-Cox檢驗??1，恒等變換?=0，對數(shù)變換???1，逆變換13來源：Andersonetc.(2007),Practitioners’guidetoGLM14?模型比較：信