University of Illinois Urbana-Champaign

Statistical inference of multivariate time series and functional data using new dependence metrics

Lee, Chung Eun

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LEE-DISSERTATION-2017.pdf

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https://hdl.handle.net/2142/98188

Description

Title
Statistical inference of multivariate time series and functional data using new dependence metrics
Author(s)
Lee, Chung Eun
Issue Date
2017-06-30
Director of Research (if dissertation) or Advisor (if thesis)
Shao, Xiaofeng
Doctoral Committee Chair(s)
Shao, Xiaofeng
Committee Member(s)
  • Simpson, Douglas
  • Li, Bo
  • Chen, Xiaohui
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2017-09-29T17:45:39Z
Keyword(s)
  • Conditional mean
  • Dimension reduction
  • Nonlinear dependence
Abstract
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.
Graduation Semester
2017-08
Type of Resource
text
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http://hdl.handle.net/2142/98188
Copyright and License Information
Copyright 2017 Chung Eun Lee

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