Minimum Bias Design for Polynomial Regression

Title & Authors
Minimum Bias Design for Polynomial Regression
Jang, Dae-Heung; Kim, Youngil;

Abstract
Traditional criteria for optimum experimental designs depend on the specifications of the model; however, there will be a dilemma when we do not have perfect knowledge about the model. Box and Draper (1959) suggested one direction to minimize bias that may occur in this situation. We will demonstrate some examples with exact solutions that provide a no-bias design for polynomial regression. The most interesting finding is that a design that requires less bias should allocate design points away from the border of the design space.
Keywords
bias;minimum bias design;Q-optimal design;integrated mean squared error(IMSE);
Language
Korean
Cited by
References
1.
Abdelbasit, K. M. and Butler, N. A. (2006). Minimum bias design for generalized linear models, The Indian Journal of Statistics, 68, 587-599.

2.
Box, G. E. P. and Draper, N. R. (1959). A bias for the selection of a response surface design, Journal of the Statistical Association, 54, 622-654.

3.
Draper, N. R. and Guttman, I. (1992). Treating bias as variance for experimental design purposes, Annals of the Institute of Statistical Mathematics, 44, 659-671.

4.
Hunga, K. and Fan, S. (2004). A note on minimum bias estimation in response surfaces, Statistics and Probability Letters, 70, 71-85.

5.
Jones, B. and Nachtsheim, C. J. (2011a). A class of three-level designs for definitive screening in the presence of second-order effects, Journal of Quality Technology, 43, 1-15.

6.
Jones, B. and Nachtsheim, C. J. (2011b). Efficient designs with minimal aliasing, Technometrics, 53, 62-71.

7.
Karson, M. J. (1970). Design criterion for minimum bias estimation of response surfaces, Journal of the Statistical Association, 65, 1565-1572.

8.
Kim, Y. (1995). A Study for additional characteristics of $I_{\lambda}$-optimal experimental designs, Communications for Statistical Applications and Methods, 2, 55-63.

9.
Montepiedra, G. and Fedorov, V. V. (1997). Minimum bias design with constraints, Journal of Statistical Planning and Inference, 63, 97-111.

10.
Myer, R. K. and Nachtsheim, C. J. (1995). The coordinate exchange algorithm for constructing exact experimental designs, Technometrics, 37, 60-69.