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

Lee, Chung Eun

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

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

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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