IDEAS home Printed from
   My bibliography  Save this article

A note on minimum bias estimation in response surfaces


  • Huang, Kuo-Nan
  • Fan, Shu-Kai S.


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.

Suggested Citation

  • Huang, Kuo-Nan & Fan, Shu-Kai S., 2004. "A note on minimum bias estimation in response surfaces," Statistics & Probability Letters, Elsevier, vol. 70(1), pages 71-85, October.
  • Handle: RePEc:eee:stapro:v:70:y:2004:i:1:p:71-85

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:70:y:2004:i:1:p:71-85. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.