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Shao, Xiaofeng Shao, Xiaofeng Simpson, Douglas Li, Bo Chen, Xiaohui Lee, Chung Eun 2017-09-29T17:45:39Z 2017-09-29T17:45:39Z 2020-03-03T10:15:25Z 2017-06-30 2017-08 In this thesis, we focus on inference problems for time series and functional data and develop new methodologies by using new dependence metrics which can be viewed as an extension of Martingale Difference Divergence (MDD) [see Shao and Zhang (2014)] that quantifies the conditional mean dependence of two random vectors. For one part, the new approaches to dimension reduction of multivariate time series for conditional mean and conditional variance are proposed by applying new metrics, the so-called Martingale Difference Divergence Matrix (MDDM), Volatility Martingale Difference Divergence (VMDDM), and vec Volatility Martingale Difference Divergence (vecVMDDM). For the other part, we propose a nonparametric conditional mean independence test for a response variable Y given a covariate variable X, both of which can be function-valued or vector-valued. The test is built upon Functional Martingale Difference Divergence (FMDD) which fully measures the conditional mean independence of Y on X. Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2019-08-01 The student, Chung Eun Lee, accepted the attached license on 2017-06-28 at 13:05. The student, Chung Eun Lee, submitted this Dissertation for approval on 2017-06-28 at 13:26. This Dissertation was approved for publication on 2017-06-30 at 14:37. DSpace SAF Submission Ingestion Package generated from Vireo submission #11275 on 2017-09-29 at 10:46:15 Made available in DSpace on 2017-09-29T17:45:39Z (GMT). No. of bitstreams: 3 LEE-DISSERTATION-2017.pdf: 1769408 bytes, checksum: 868d0f3001c6f367730c72fa7e26d8c6 (MD5) LICENSE.txt: 4210 bytes, checksum: 9c30257595230ec17a67adb23e7bf077 (MD5) PROQUEST_LICENSE.txt: 4556 bytes, checksum: 6defecdcb4c170f4fe2ad37ee192d861 (MD5) Previous issue date: 2017-06-30 Embargo set by: Colleen Fallaw for item 103489 Lift date: 2019-09-29T17:48:06Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 103489 Lift date: 2020-03-02T19:56:41Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 103489 Lift date: 2020-03-02T19:59:52Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 103489 Lift date: 2020-03-02T20:02:46Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system U of I Only Restriction Lifted for Item 103489 on 2020-03-03T10:15:25Z. application/pdf http://hdl.handle.net/2142/98188 en Copyright 2017 Chung Eun Lee Conditional mean Dimension reduction Nonlinear dependence Statistical inference of multivariate time series and functional data using new dependence metrics text text Statistics Statistics University of Illinois at Urbana-Champaign Dissertation Ph.D.