Behavior of Elemental Sets in Regression

Authors

David J. Olive, Southern Illinois University CarbondaleFollow
Douglas M. Hawkins, University of Minnesota - Twin Cities

Comments

Published in Statistics & Probability Letters, 77, 621-624. doi: 10.1016/j.spl.2006.09.009

Abstract

Elemental sets are used to produce trial estimates b of the regression coefficients β. If b₀ minimizes ||b-β|| among all elemental fits b, then ||b₀-β||=O_P(n^-1), regardless of the criterion used. For any estimator b_A, ||b_A-β|| is at best O_P(n^-1/2). Hence restricting fits to elemental introduces asymptotically negligible error.

Recommended Citation

Olive, David J. and Hawkins, Douglas M. "Behavior of Elemental Sets in Regression." (Mar 2007).