Browse > Article

MEASURES FOR STABILITY OF SLOPE ESTIMATION ON THE SECOND ORDER RESPONSE SURFACE AND EQUALLY-STABLE SLOPE ROTATABILITY  

Park, Sung H. (Department of Statistics, Seoul National University)
Kang, Ho-Seog (System Business Co. LTD.)
Kang, Kee-Hoon (Department of Statistics, Hankuk University of Foreign Studies)
Publication Information
Journal of the Korean Statistical Society / v.32, no.4, 2003 , pp. 337-357 More about this Journal
Abstract
This paper introduces new measures for the stability of slope estimation on the second order response surface at a point and on a sphere. As a measure of point stability of slope estimation, we suggest a point dispersion measure of slope variances over all directions at a point. A spherical dispersion measure is also proposed as a measure of spherical stability of slope estimation on each sphere. Some designs are studied to explore the usefulness of the proposed measures. Using the point dispersion measure, another concept of slope rotatability called equally-stable slope rotatability is proposed as a useful property of response surface designs. We provide a set of conditions for a design to have equally-stable slope rotatability.
Keywords
Point dispersion measure; spherical dispersion measure; spherical point dispersion measure; spherical rotation dispersion measure;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Minimizing the maximum variance of the difference between two estimated responses /
[ Huda,S.;Mukerjee,R. ] / Biometrika   ScienceOn
2 The design of experiments to estimate the slope of a response surface /
[ Atkinson,A.C. ] / Biometrika   ScienceOn
3 Minimax designs for estimating the slope of a secondorder response surface in a cubic region /
[ Huda,S.;Shafiq,M. ] / Journal of Applied Statistics
4 Graphical assessment of the prediction capability of response surface designs /
[ Giovannitti-Jensen,A.;Myers,R.H. ] / Technometrics   ScienceOn
5 Slope-rotatable central composite designs /
[ Hader,R.J.;Park,S.H. ] / Technometrics   ScienceOn
6 A measure and a graphical method for evaluating slope rotatability in response surface designs /
[ Jang,D.H.;Park,S.H. ] / Communications in Statistics-Theory and Methods   ScienceOn
7 Multi-factor experimental designs for exploring response surfaces /
[ Box,G.E.P.;Hunter,J.S. ] / Annals of Mathematical Statistics   ScienceOn
8 The behavior of the variance function of the difference between two estimated responses /
[ Herzberg,A.M. ] / Journal of the Royal Statistical Society
9 The variance function of the difference between two estimated responses /
[ Box,G.E.P.;Draper,N.R. ] / Journal of the Royal Statistical Society
10 A note on slope rotatability over all directions /
[ Draper,N.R.;Ying,L.H. ] / Journal of Statistical Planning and Inference   ScienceOn