Optimum Designs for Polynomial Extrapolation

Robust Designs for Approximately Polynomial Regression Abbreviated title: Robust Polynomial Designs

Abstract We study designs for the regression model E[Y jx] = Pp 1 j=0 jx+x (x), where (x) is unknown but bounded in absolute value by a given function (x). This class of response functions models departures from an exact polynomial response. We consider the construction of designs which are robust, with respect to various criteria, as the true response varies over this class. The resulting desi...

Polynomial techniques for investigation of spherical designs

We investigate the structure of spherical τ -designs by applying polynomial techniques for investigation of some inner products of such designs. Our approach can be used for large variety of parameters (dimension, cardinality, strength). We obtain new upper bounds for the largest inner product, lower bounds for the smallest inner product and some other bounds. Applications are shown for proving...

Approximate Optimal Designs for Multivariate Polynomial Regression

Abstract: We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically the approximate optimal design problem. The geometry of the design is recovered via semidefinite programming duality theory. Th...

On Optimum Designs of Universal Switch Blocks

This paper presents a breakthrough decomposition theorem on routing topology and its applications in the designing of universal switch blocks. A switch block of k sides and W terminals on each side is said to be universal (a (k, W )-USB) if it is routable for every set of 2-pin nets with channel density at most W . The optimum USB design problem is to design a (k, W )-USB with the minimum numbe...

Heteroscedastic T-Optimum Designs for Multiresponse Dynamic Models