**Sankhya: The Indian Journal of Statistics**

1996, Volume 58, Series B, Pt. 3, pp. 396--406

**ON THE CHOICE OF A UNIFORM DESIGNS IN POLYNOMIAL REGRESSION MODELS**

By

WENG KEE WONG, *University of California, Los Angeles*

SUMMARY. This paper examines the performance of uniform designs under a variety of experimental conditions. Robustness of these designs to various model assumptions in terms of D and G-efficiencies are assessed, including the effect of having too few or too many points in the design. It is shown that the optimum number of support points of the uniform design should be about one more than the degree of the assumed polynomial model if the assumed degree is less than 6, and about twice the assumed degree if the assumed degree is between 6 and 10.

A related efficiency useful for estimating the coefficient of the highest term in the polynomial model is similarly studied.

*AMS (1991) subject classification.* 62K05.

*Key words and phrases.* Approximate designs, bias, $D$ and $G$-optimality, homoscedasticity.