On the robustness of balanced fractional 2m factorial designs of resolution 2l+1 in the presence of outliers
- 12 Downloads
By use of the algebraic structure, we obtain a simplified expression for the outlier-insensitivity factor for balanced fractional 2m factorial (2m-BFF) designs of resolution 2l+1 derived from simple arrays (S-arrays), whose measure has been introduced by Ghosh and Kipnegeno (1985,J. Statist. Plann. Inference,11, 119–129). It is defined by use of the measure suggested by Box and Draper (1975,Biometrika, 62 (2), 347–352). As examples, we study the sensitivity ofA-optimal 2m-BFF designs of resolution VII (i.e.,l=3) given by Shirakura (1976,Ann. Statist.,4, 515–531; 1977,Hiroshima Math. J.,7, 217–285). We observe that these designs are robust in the sense that they have low sensitivities.
Key words and phragesOutliers sensitivities A-optimal designs projection matrices
Unable to display preview. Download preview PDF.
- Chopra, D. V. (1975). Balanced optimal 28 fractional factorial designs of resolution V, 52<N<59,A Survey of Statistical Design and Linear Models (ed., J. N. Srivastava), North-Holland, Amsterdam, 91–100.Google Scholar
- Yamamoto, S., Shirakura, T., and Kuwada, M. (1976) Characteristic polynomials of the information matrices of balanced fractional 2m factorial designs of higher (2l+1) resolution,Essays in Probability and Statistics (eds., S. Ikeda et al.), Shinko Tsusho, Tokyo, 73–94.Google Scholar