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Title:Statistical inference of multivariate time series and functional data using new dependence metrics
Author(s):Lee, Chung Eun
Director of Research:Shao, Xiaofeng
Doctoral Committee Chair(s):Shao, Xiaofeng
Doctoral Committee Member(s):Simpson, Douglas; Li, Bo; Chen, Xiaohui
Department / Program:Statistics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(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.
Issue Date:2017-06-30
Rights Information:Copyright 2017 Chung Eun Lee
Date Available in IDEALS:2017-09-29
Date Deposited:2017-08

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