Related papers: The Asymptotics of Optimal Designs for Polynomial …
We present a new approach to the design of D-optimal experiments with multivariate polynomial regressions on compact semi-algebraic design spaces. We apply the moment-sum-of-squares hierarchy of semidefinite programming problems to solve…
We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The…
We revisit the classical problem of optimal experimental design (OED) under a new mathematical model grounded in a geometric motivation. Specifically, we introduce models based on elementary symmetric polynomials; these polynomials capture…
Optimal designs are required to make efficient statistical experiments. D-optimal designs for some models are calculated by using canonical moments. On the other hand, integrable systems are dynamical systems whose solutions can be written…
In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal…
The theory of optimal design of experiments has been traditionally developed on an Euclidean space. In this paper, new theoretical results and an algorithm for finding the optimal design of an experiment located on a Riemannian manifold are…
Improvements in technology lead to increasing availability of large data sets which makes the need for data reduction and informative subsamples ever more important. In this paper we construct $ D $-optimal subsampling designs for…
We characterize $D$-optimal designs in the two-dimensional Poisson regression model with synergetic interaction and provide an explicit proof. The proof is based on the idea of reparameterization of the design region in terms of contours of…
The experimental design problem concerns the selection of k points from a potentially large design pool of p-dimensional vectors, so as to maximize the statistical efficiency regressed on the selected k design points. Statistical efficiency…
In this note we consider the optimal design problem for estimating the slope of a polynomial regression with no intercept at a given point, say z. In contrast to previous work, which considers symmetric design spaces we investigate the…
We consider the problem of constructing optimal designs for population pharmacokinetics which use random effect models. It is common practice in the design of experiments in such studies to assume uncorrelated errors for each subject. In…
A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for $D$-optimal criterion on continuous design spaces are…
Optimal design theory for nonlinear regression studies local optimality on a given design space. We identify designs for the Bradley--Terry paired comparison model with small undirected graphs and prove that every saturated D-optimal design…
In this work, we propose a novel sampling method for Design of Experiments. This method allows to sample such input values of the parameters of a computational model for which the constructed surrogate model will have the least possible…
In this paper we construct (locally) $D$-optimal designs for a wide class of non-linear multiple regression models, when the design region is a $k$-dimensional ball. For this construction we make use of the concept of invariance and…
The c-functions, related to a reductive symmetric space G/H and a fixed representation of a maximal compact subgroup K of G, are shown to satisfy polynomial bounds in imaginary directions.
We discuss the optimal design problem in regression models with long-range dependence error structure. Asymptotic optimal designs are derived and it is demonstrated that these designs depend only indirectly on the correlation function.…
We formulate explicit predictions concerning the symmetry of optimal codes in compact metric spaces. This motivates the study of optimal codes in various spaces where these predictions can be tested.
We find t-designs on compact algebraic manifolds with a number of points comparable to the dimension of the space of polynomials of degree t on the manifold. This generalizes results on the sphere by Bondarenko, Radchenko and Viazovska. Of…
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…