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oai:www.ideals.illinois.edu:2142/45543 2023-07-11 col_2142_17362 col_2142_5131 com_2142_17361 com_2142_8903 com_2142_5130

Shao, Xiaofeng Shao, Xiaofeng Qu, Annie Koenker, Roger W. Chen, Yuguo Zhang, Xianyang 2013-08-22T16:47:13Z 2013-08-22T16:47:13Z 2015-08-22T10:00:54Z 2013-08 2013-08-22T16:47:13Z 2013-08 Functional data Analysis has emerged as an important area of statistics which provides convenient and informative tool for the analysis of data objects of high dimension/high resolution. In the literature, it seems that the emphasis has been placed on independent functional data or models where the covariates and errors are assumed to be independent. However, the independence assumption is often too strong to be realistic in many application especially if the data are collected sequentially over time such as climate data and high frequency financial data. Motivated by our ongoing research on the development of high-resolution climate projections through statistical downscaling, we consider the change point problem and the two sample problem for temporally dependent functional data. Specifically, in Chapter 1, we develop a self-normalization based test to test the structural stability of temporally dependent functional observations. We propose new tests to detect the differences of the covariance operators and their associated characteristics of two functional time series in Chapter 2. The self-normalization approach introduced in the first two chapters is closely linked to the fixed-b asymptotic scheme in the econometrics literature. Motivated by recent studies on heteroskedasticity and autocorrelation consistent based robust inference, we propose a class of estimators for estimating the asymptotic covariance matrix of the generalized method of moments estimator in the stationary time series models in Chapter 3. Under mild conditions, we establish the first order asymptotic distribution for the Wald statistics when the smoothing parameter is held fixed. Furthermore, we derive higher order Edgeworth expansions for the finite sample distribution of the Wald statistics in the Gaussian location model under the fixed-smoothing paradigm. The results are used to justify the second order correctness of a new bootstrap method, the Gaussian dependent bootstrap, in the context of Gaussian location model. Finally, in Chapter 4, we describe an extension of the fixed-b approach to the empirical likelihood estimation framework. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2013-06-18T18:42:38Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Zhang_Xianyang.pdf: 1479042 bytes, checksum: 5122e88063dc091909441927f7093057 (MD5) Made available in DSpace on 2013-08-22T16:47:13Z (GMT). No. of bitstreams: 2 Xianyang_Zhang.pdf: 1482951 bytes, checksum: 3cf3b25778f229755dca998f45b3e31e (MD5) license.txt: 4064 bytes, checksum: 2a6221a51a5cb5a624eaa0f5f63abf86 (MD5) Restriction data tranferred 2014-07-01T11:20:44-05:00 Original Data Group with Access UIUC Users [automated] Release Date: 2015-08-22 11:49:27 UTC Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Seth Robbins (srobbins@illinois.edu) on 2013-08-22T16:49:32Z Item is restricted until 2015-08-22T16:49:27Z U of I Only Restriction Lifted for Item 45525 on 2015-08-22T10:00:54Z. http://hdl.handle.net/2142/45543 en Copyright 2013 Xianyang Zhang Functional data Change-point problem Two sample problem Self-normalization High order expansion Bootstrap Empirical likelihood Statistical inference for dependent data text Statistics 1583 Statistics 0329 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Statistics -UIUC 10KS0329PHD