On the equivalence of three estimators for dispersion effects in unreplicated two-level factorial designs


van de Ven, P.M. (2007) On the equivalence of three estimators for dispersion effects in unreplicated two-level factorial designs. Journal of Statistical Planning and Inference, 18-29. (doi:10.1016/j.jspi.2007.05.026).

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Description/Abstract

Box and Meyer [1986. Dispersion effects from fractional designs. Technometrics 28(1), 19–27] were the first to consider identifying both location and dispersion effects from unreplicated two-level fractional factorial designs. Since the publication of their paper a number of different procedures (both iterative and non-iterative) have been proposed for estimating the location and dispersion effects. An overview and a critical analysis of most of these procedures is given by Brenneman and Nair [2001. Methods for identifying dispersion effects in unreplicated factorial experiments: a critical analysis and proposed strategies. Technometrics 43(4), 388–405]. Under a linear structure for the dispersion effects, non-iterative estimation methods for the dispersion effects were proposed by Brenneman and Nair [2001. Methods for identifying dispersion effects in unreplicated factorial experiments: a critical analysis and proposed strategies. Technometrics 43(4), 388–405], Liao and Iyer [2000. Optimal 2n-p fractional factorial designs for dispersion effects under a location-dispersion model. Comm. Statist. Theory Methods 29(4), 823–835] and Wiklander [1998. A comparison of two estimators of dispersion effects. Comm. Statist. Theory Methods 27(4), 905–923] (see also Wiklander and Holm [2003. Dispersion effects in unreplicated factorial designs. Appl. Stochastic. Models Bus. Ind. 19(1), 13–30]). We prove that for two-level factorial designs the proposed estimators are different representations of a single estimator. The proof uses the framework of Seely [1970a. Linear spaces and unbiased estimation. Ann. Math. Statist. 41, 1725–1734], in which quadratic estimators are expressed as inner products of symmetric matrices.

Item Type: Article
Additional Information: International Conference on Design of Experiments (ICODOE), edited by Sudhir Gupta, Manohar Aggarwal and Lih-Yuan Deng
ISSNs: 0378-3758 (print)
Related URLs:
Keywords: location-dispersion model, mixed linear model, fractional factorial designs
Subjects: Q Science > QA Mathematics
H Social Sciences > HA Statistics
Divisions: University Structure - Pre August 2011 > Southampton Statistical Sciences Research Institute
University Structure - Pre August 2011 > School of Mathematics > Statistics
ePrint ID: 46482
Date Deposited: 04 Oct 2007
Last Modified: 27 Mar 2014 18:30
Contact Email Address: pvdv1e06@soton.ac.uk
URI: http://eprints.soton.ac.uk/id/eprint/46482

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