A note on minimum bias estimation in response surfaces

Kuo-Nan Huang and Shu-Kai S. Fan

Statistics & Probability Letters, 2004, vol. 70, issue 1, 71-85

Abstract: This paper presents a supplementary, valuable property of the minimum bias estimation (MBE) procedure, addressed in Karson et al. (Technometrics 11 (1969) 461), within the context of a single variable design problem appearing in the response surface methodology (RSM) literature. It is discovered that this simple property only depends on the relationship between the total number of experimental runs and the number of center replicates. Illustrations of the design property are given for a certain simple model of single design variable and design settings, and the comparison of results between the MBE approach and Box and Draper's (J. Amer. Statist. Assoc. 54 (1959) 622) approach are reported by using the average mean squared error (AMSE) value as the performance criterion. Apart from being additional comments on the MBE approach, the research outcome in this study can also serve as a look-up guide for RSM practitioners to choose a suitable estimation approach between the Box and Draper's and MBE approaches, and then arrange better design allocation to achieve optimum AMSE values under different potential bias errors for the single variable design problem.

Keywords: Minimum; bias; estimation; (MBE); Response; surface; methodology; (RSM); Average; mean; squared; error; (AMSE); Least-squares; estimation; (LSE); Center; runs (search for similar items in EconPapers)
Date: 2004
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