扩散过程的统计推断以及经验似然方法在高维问题中的应用

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1、UNIVEGRNSIIKTEYP1898ÆÆƬ¬¬ïïïÄÄÄ)))ÆÆÆØØØ©©©K8µ***ÑÑÑLLL§§§ÚÚÚOOOíííäää±±±999²²²qqq,,,{{{333ppp¯¯¯KKK¥¥¥AAA^^^6¶µ~AÆÒµ1101110800Xµ1u+nÆ;µÚOÆïĵûÖÚO6¶µt¿ÇncÊ(²?ÛÂÚ+Ø©«üÚ<§²Ø©öÓ¿§ØòØ©=/¦<§½Ø¿E!¹!ûì½±?ÛªDÂ"ÄK§ÚåkNöͯK§òU«ú{ÆI?"*ÑL§ÚOíä±9²q,{3p¯K¥A^~AÚOÆ6¶µt¿ÇÁØ©)üÜ©:1Ü©´

2、1Ù,1Ü©)1ÙÚ1nÙ.1Ü©ÌÄé*ÑL§ëê?1ÚOíä,ù´7KOþÆpK;1Ü©Ìùã²q,{3p¯K¥A^.du*ÑL§=£Ý¼êÏ~¿ØäkwªLª,ù¦DÚ4q,O¿ØU^uéAëê?1O.·¦^A¨ıt-Sahalia(1999,2002){é*ÑL§=£Ý¼ê?1Cq,,ÄuTCqACq4q,O.TOÚO531Ù¥Ñ.31Ù¥,·Äp2²q,{3'êâ¥A^.3ùÙ¥,·bëêdO§(½.·Ä3O§ê!ëêê±9*ÿêþUXþuÑ,Ó*ÿm3'5½e,XÛ$^2²q,{éëê?1O.31nÙ¥,·ù

3、ã)ºCþêXþêO,XÛ$^²q,{épCþ?1çÀ.DÚCþçÀ{ØÓ,·uyCþçÀ¯Kþdubu¯K.ù#*:¦·{®k{'¿ØIé?Û'ëê?1O,Ó·{äkÀJ5.'cµ*ÑL§,²q,,pêâ©Û,f'êâ,Cqq,O,CþçÀ,ÚOíäInferenceonDiffusionProcessesandApplicationofEmpiricalLikelihoodinHighDimensionalSettingJinyuanChang(Statistics)SupervisedbySongXiChenAbstractTherearetwoparts

4、inthisthesis.Thefirstpartischapter1,andthesecondoneiscomposedofchapter2andchapter3.Forthefirstpart,weconsiderthestatisticalinferenceondiffusionprocesses,whichisanimportanttopicinfinancialeconomet-rics.Thesecondpartisconcernedwiththeapplicationofempiricallikelihoodinhigh-dimensionalsetting.Asthetransitio

5、ndensityfunctiondoesnothaveanexplicitformintheusualcase,itpreventstheapplicationofclassicalmaximumlikelihoodestimationforcorrespondingparameters.WefollowtheapproachproposedbyA¨ıt-Sahalia(1999,2002)toapproximatethetransitiondensityfunction,andobtaintheestimatorbasedonsuchapproximation.Thetheoreticalp

6、ropertiesofthisestimatorisgiveninchapter1.Inchapter2,weconsidertheapplicationofhigh-dimensionalempiricallikelihoodondependentdata.Theparametersofinterestareassumedtosatisfygeneralestimatingequations.Underthesettingthatthenumberofestimatingequations,dimensionsofparametersandcovariatesalldivergewithth

7、esamplesize,aswellasthereexistsdependenceamongthedata,weconsiderestimatingtheparametersviathegeneralizedempiricallikelihood.Inchapter3,weproposeanewfeaturescreeningapproachforultra-high-dimensionaldat