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

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2017

Author dc:creator

• Lee, Chung Eun

Contributors dc:contributor

• Shao, Xiaofeng
• Simpson, Douglas
• Li, Bo
• Chen, Xiaohui

• Conditional mean
• Dimension reduction
• Nonlinear dependence

Statement dc:rights

• Copyright 2017 Chung Eun Lee

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/98188