Variance Function Estimation in Regression: The Effect of Estimating the Mean
Abstract
The authors consider estimation of a variance function g in regression problems. Such estimation requires simultaneous estimation of the mean function f. We obtain sharp results on the extent to which the smoothness of f influences best rates of convergence for estimating g. For example, in nonparametric regression with two derivatives on g, classical rates of convergence are possible if and only if the unknown f satisfies a Lipschitz condition of order 1/3 or more. If a parametric model is known for g, then g may be estimated n 1/2 - consistently if and only if f is Lipschitz of order 1/2 or more. Optimal rates of convergence are attained by kernel estimators.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1988
- Accession Number
- ADA198228
Entities
People
- Peter Hall
- R. J. Carroll
Organizations
- Texas A&M University