文档介绍：Bootstrap?{9ùA^ ? ??< f 2 ??6?9? ü???? ???? ê??O???????;? V???ênúO ???? ??L§9ùA^ ? ???O n?a? ? ??ü ???? ??J?F? Bootstrap methods and their applications Candidate Ping Mao Supervisor Professor Hanjun Zhang College School of Mathematics putational Science Program Probability and Statistics Specialization Stochastic Processes and Their Applications Degree Master of Science University Xiangtan University Date April 15th, 2013 ???? ????M5(2 ?<x-(2μ¤￥????′?<3?????e?á?1?? ¤?????¤J"? ?￥AO\±I5ú^?SN §????? 1??ù|?<?8N?2uL?>??¤J??"é??????? -??z??<ú8N§t?3?￥±2(?aI2"?<???￡??(2?{??Jd?<?ú" ??\?μ F?μ c ? F ?????|^??? ????????)??k'?3!|^????5?§ó? ???3??I[k'ü????x????E<?ú>f?§#N? ????ú/?"?<???????±ò?? ????ü?ü?S N?\k'êa￥?1u￠§?±?^K<!<?×￡?E????ú??????" ????U??5??n" ??\?μ F?μ c ? F ??\?μ F?μ c ? F á ? Bootstrap?{′úOí?￥μ?úU?úOt°Y???-???{.gEfron ?gJ??8§ùn?NX??3???uDú??.??òBootstrap?{2? ?$^u??+??￠SˉK???￥§~X7K!??!?ˉ!n!I[??! )?????.??ì?éBootstrap?{? ???o(!?? n??O?& ?m?{3VaRO?￥?A^±9éBootstrap?{?v?U?. 1?ù′X?ü?§ì??? Bootstrap?{?n????μ!??{¤! ??yGú????¤??ì?(?. 1?ù0? Bootstrap?{???g?!ì??K!°(5±9§?`":. 1nù??o( ?uBootstrap?IO???O!??u?ú￡8?.. 1où?? Bootstrap-t!z? !BCaùn??uBootstrap?O?&?m ??{. 1êù0?ox??￡VaR¤???!VaR?O??{±91oùn??O? &?m?{?￠y??§???Bootstrap-t!z? !BCaùn??uBootstrap ?&?m??{`uVaRDú?O??{. 18ù′éBootstrap?{"????U?. 'cμg?{?V??ù?IO???O???u??￡8??&?m?ox??? °(Y I Abstract Bootstrap methods are important ways to evaluate and improve the accuracy of statistics in statistical inference. Since Efron presented for the ?rst time, their theoretical system developed and improved in continuous. The Bootstrap methods are extensively applied in all ?elds. For example, ?nancial, medical, military, foreign trade, ?nance, biomedicine and so on. In this thesis, we made prehensive summary of the bootstrap methods, applications of three methods for the estimate of con?dence intervals in the calculation of VaR, and the improvement of bootstrap methods. In the ?rst chapter, the theoretical researc