Nonparametric regression with dependent errors

Date
1997
Authors
Yang, Yuhong
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Altmetrics
Authors
Research Projects
Organizational Units
Statistics
Organizational Unit
Journal Issue
Series
Department
Statistics
Abstract

We study minimax rates of convergence for nonparametric regression under a random design with dependent errors. It is shown that when the errors are independent of the explanatory variables, long-range dependence among the errors does not necessarily hurt regression estimation, which at first glance contradicts with earlier results by Hall and Hart, Wang, and Johnstone and Silverman under a fixed design. In fact we show that, in general, the minimax rate of convergence under the square L2 loss is simply at the worse of two quantities: one determined by the massiveness of the class alone and the other by the severity of the dependence among the errors alone. The clear separation of the effects of the function class and dependence among the errors in determining the minimax rate of convergence is somewhat surprising. Examples of function classes under different covariance structures including both short- and long-range dependences are given.

Comments

This preprint was published as Yuhong Yang, "Nonparametric Regression with Dependent Errors", Bernoulli (2001): 633-655.

Description
Keywords
Citation
DOI
Source
Collections