Asymptotically optimal difference-based estimation of variance in nonparametric regression

Hall, P., Kay, J.W. and Titterington, D.M. (1990) Asymptotically optimal difference-based estimation of variance in nonparametric regression. Biometrika, 77(3), pp. 521-528. (doi: 10.1093/biomet/77.3.521)

Abstract

We define and compute asymptotically optimal difference sequences for estimating error variance in homoscedastic nonparametric regression. Our optimal difference sequences do not depend on unknowns, such as the mean function, and provide substantial improvements over the suboptimal sequences commonly used in practice. For example, in the case of normal data the usual variance estimator based on symmetric second-order differences is only 64% efficient relative to the estimator based on optimal second-order differences. The efficiency of an optimal mth-order difference estimator relative to the error sample variance is 2m/(2m + 1). Again this is for normal data, and increases as the tails of the error distribution become heavier.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Titterington, Professor D and Hall, Professor Peter and Kay, Dr James
• Authors: Hall, P., Kay, J.W., and Titterington, D.M.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: Biometrika
• Publisher: Oxford University Press
• ISSN: 0006-3444
• ISSN (Online): 1464-3510