Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series B, Pt. 2, 239--248

ON A SIMPLE BIAS BOUND FOR RESPONSE SURFACE ESTIMATORS

By

STEPHAN MORGENTHALER, E P F Lausanne

 

SUMMARY. This paper discusses a simple bound for the bias of any response surface estimator that is linear in the observations. This bound is valid whenever the norm of the gradient of the true surface is bounded and can be generalised to higher derivatives. At any given point, it is computed as a weighted sum of the distances to the design points with the weights given by the absolute values of the estimation weights. The paper also considers the application of the bias bound in analysing the quality of a given design.

AMS subject classification. 62K99

Key words and phrases. Biased response surfaces, design diagnostics, design optimality

FULL PAPER.

This article in Mathematical Reviews.