Three essays on nonparametric inference for longitudinal data and time series data.

Open Access
Author:
Kim, Seonjin
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
June 05, 2013
Committee Members:
  • Zhibiao Zhao, Dissertation Advisor
  • Zhibiao Zhao, Committee Chair
  • Runze Li, Committee Member
  • Donald Richards, Committee Member
  • Fuqing Zhang, Committee Member
  • Jingzhi Huang, Special Member
Keywords:
  • Locally stationary process
  • Longitudinal data
  • Measurement errors
  • Nonparametric inference
  • Quantile regression
  • Time series
Abstract:
This thesis consists of three essays on nonparametric inference problems for dependent data, such as longitudinal data and time series data. In the literature on statistical estimation and inference, the frequently imposed independence assumption allows for technical simplicity, but it leads to serious restrictions in many applications. For example, in longitudinal data analysis and time series analysis, dependence is actually one of the main objectives of interest. The techniques developed for independent data may fail or not be efficient where dependence presents. Moreover, the traditional approach to nonparametric inference problems has some disadvantages due to the structure dependency and estimation difficulty of the limiting variance function, and there exist mathematical obstacles caused by dependence inherited in data. In order to alleviate the aforementioned problems, I have developed novel theories and methodologies for dependent data through self-normalization techniques and quantile regression. The developments involve theoretical notability as well as practical applicability for financial, medical, environmental, and social science.