| GLIVENKO-CANTELLI TYPE THEOREMS ANDTHEIR APPLICATIONS |
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| 作者姓名： | 朱力行 |
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| 作者单位： | Probability Laboratory，Institute of Applied Mathematics. Chinese Academy of Sciences，Beijing 100080，China |
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| 摘 要： | 1IntroductionLet(S,yi)beameasurablespacealldletPbeaprobabilitymeasureon(S,yi).I,et{Xi,i21}bei.i.d.S--valuedrandolllvariableswitllcommonlawP,Pc,istheempiricalmeasurebasedonXI,',X,,.OneofthelllostpersistentproblemsinprobabilityandstatisticsisthatoffindingoutthelawPfi,onltherandomlawP,,.Thea.s.convergenceofPntoPuniformlyoverclassesoffunctionsisasubjectofparticularinterest,thefundamentalresultisthecelebratedGlivenko-Cantellitlleorm.TheworkofVapnikandC.,..u..ki,5](1971)vitalizestilestudy…
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GLIVENKO-CANTELLI TYPE THEOREMS AND THEIR APPLICATIONS |
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| Zhu Lixing.GLIVENKO-CANTELLI TYPE THEOREMS ANDTHEIR APPLICATIONS[J].Acta Mathematica Scientia,1997(3). |
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| Authors: | Zhu Lixing |
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| Abstract: | In this paper, we present a sufficient condition for uniform convergence of means to their expectations over the classes of real functions.Our proof is very simple via connecting this convergence to uniform convergence over the class of indicator functions. Furthermore, we obtain a convergent result concerning a non=VC class with an application to variable transformation for fitting regression model. |
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| Keywords: | Uniform convergence non-VC class of functions variable transformation method |
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