S. Huda

Minimax designs for estimating the slope of a third-order response surface in a hypercubic region

The design criterion considered is minimization of the variance of the estimated slope of a response surface maximized over all points in the factor space. Optimal designs under the minimax criterion, within some classes of commonly used designs, are derived for third-order polynomial models over hypercubic regions.

Fourth-order rotatable designs: A-optimal measures

The A-optimal rotatable design measures are derived for fourth-order polynomial regression on hyperspheres. The application of the association algebra of triangular association scheme is helpful in the derivation of the objective function.

On D- and E- minimax optimal designs for estimating the axial slopes of a second-order response surface over hypercubic regions

Design of experiments for estimating the slopes of a response surface is considered. Design criteria analogous to the traditional ones but based upon the variance-covariance matrix of the estimated slopes along factor axes are proposed. Optimal designs under the proposed criteria are derived for second-order polynomial regression over hypercubic regions. Best de¬signs within some commonly used classes of designs are also obtained and their efficiencies are investigated.

Minimax second-order designs over hypercubes for the difference between estimated responses at a point and at the centre

Minimization of the variance of the difference between estimated response at a point and that at the centre maximized over all points in the experimental region is taken as the design criterion. Optimal designs are derived for second-order polynomial models over hypercubes. The performance of best designs among the symmetric product designs and the star point designs is investigated.

On some DS-optimal designs in spherical regions

For polynomial regression over spherical regions the d-th order Ds-optimal designs for the λ-th order models are derived for 1 ≤ λ ≤ d ≤ 4. Efficiencies of these designs with respect to the λ-th order D-optimal designs are obtained. The effects of estimating addtional parameters due to an m-th order model (d ≥ m >>λ) on the efficiencies are investigated.

D-optimal measures for fourth-order rotatable designs

This paper derives D-optimai measures for fourth-order rotatable designs. The objective function is seen to be separable and this is helpful in the derivation

Optimal weighing designs: approximate theory

Approximate theory employing FBECHET derivative is utilized to derive optimal weighing designs under D- and A-optimality criteria. Both spring and chemical balance designs, without and with restriction on the number of objects that may be includ¬ed in a weighing, are considered. The optimality of some exact (discrete) designs is demonstrated

Optimal statistical designs with circular string property

This paper develops an approximate theory for D- and A-optlmal statistical designs with a circular string property. It is shown how the problems of deriving optimal designs can be reduced to non-linear programming problems involving small numbers of decision variables. The results are seen to be helpful in dealing with the exact design problem with a finite number of obser vations.

Minimax second-order designs for difference between estimated responses in extrapolation region

Minimization of the variance of the difference between estimated response at two response at two points maximized over all pairs of points in the extrapolation region is taken as the criterion for selecting designs. Optimal designs under the criterion are derived for second-order models.

On optimal designs with restricted circular string property

Abstract Exact optimality results on minimal statistical designs with circular string property under restriction are derived. Optimal approximate designs are also obtained.