Estimation and forecasting methodologies for nonparametric regression models via dynamic linear models

Open Access
Author:
Jiang, Yuejiao
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
June 15, 2009
Committee Members:
  • Runze Li, Dissertation Advisor
  • Jingzhi Huang, Committee Member
  • Murali Haran, Committee Member
  • Aleksandra B Slavković, Committee Member
  • Runze Li, Committee Chair
Keywords:
  • nonparametric regression models
  • dynamic linear models
Abstract:
Nonparametric regression models have been used to explore features of data. Various estimation procedures have been proposed for estimating nonparametric regression models in the literature. The existing procedures may enjoy some statistically optimal properties, but it is difficult to use the estimated regression functions for the purpose of forecasting, i.e., prediction with independent variables beyond the observed range. Motivated by dynamic linear model estimation and forecasting methodologies developed by citeA{west1997}, our research extends the study in two directions by building connections between nonparametric regression models and dynamic linear models. First, for nonparametric regression models with independently and identically distributed errors, we develop a regularized regression spline to determine hyper-parameter values for errors and compare estimation performance with a local linear estimator, a commonly used smoothing method for nonparametric regression. Second we study nonparametric regression models with autoregressive errors process since when collected over time, data are likely to be serially correlated. From our simulation studies, the proposed methods outperform the local linear regression under certain statistical settings for both models with i.i.d. and autoregressive error. Last, we establish a connection between varying coefficient models and dynamic linear models. % what are "certain statistical settings" ? % with an autoregressive error process. We %provide some insights into the selection of hyper-parameter in the %varying coefficient models to save computing time. Both estimation and forecasting performances of the proposed method are examined via simulations. The proposed methods perform well for larger sample sizes. The proposed procedures are demonstrated by analysis of two real data examples.