Local Modeling For Data With Autocorrelations

Open Access
Author:
Li, Yan
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
December 16, 2007
Committee Members:
  • Runze Li, Committee Chair
  • Naomi S Altman, Committee Member
  • David Russell Hunter, Committee Member
  • Jingzhi Huang, Committee Member
Keywords:
  • Multivariate
  • Autoregressions
  • Nonoparametric models
  • Variable Selection
Abstract:
Motivated by a study on how the levels of air pollutants affect the number of daily hospital admissions for circulatory and respiratory in Hong Kong, we propose new procedures for nonparametric regression models and varying coefficient models with auto-regressive (AR) errors. As a data-analytical approach, nonparametric regression has become popular to explore the fine data feature. However, most existing nonparametric regression methods do not consider correlated errors. From our limited experience, ignoring the correlation within the random errors typically yields an undesired results. We propose new estimation procedures which take into account the correlation by using profile least squares techniques. We further propose a new order selection procedure to determine the order of AR errors by using penalized profile least squares approach with the smoothly clipped absolute deviation (SCAD, Fan and Li, 2001). Under certain regular conditions, the asymptotic properties of the resulting estimates are derived. Some numerical comparisons are conducted by Monte Carlo simulation. The proposed methodology is illustrated by an analysis of a real data set.