Related papers: An Approximate Approach to E-optimal Designs for W…
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…
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 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…
For a broad class of nonlinear regression models we investigate the local E- and c-optimal design problem. It is demonstrated that in many cases the optimal designs with respect to these optimality criteria are supported at the Chebyshev…
Optimal designs can help experimenters obtain more accurate parameter estimates with reduced experimental time and cost. In this paper, we characterize the Expected Weighted (EW) D-optimal designs as robust designs against unknown parameter…
We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…
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…
Consider the problem of constructing an experimental design, optimal for estimating parameters of a given statistical model with respect to a chosen criterion. To address this problem, the literature usually provides a single solution.…
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…
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…
This paper considers the problem of constructing optimal discriminating experimental designs for competing regression models on the basis of the T-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975) 57-70].…
We present a unified deterministic approach for experimental design problems using the method of interlacing polynomials. Our framework recovers the best-known approximation guarantees for the well-studied D/A/E-design problems with simple…
The generalized linear models (GLMs) are widely used in statistical analysis and the related design issues are undoubtedly challenging. The state-of-the-art works mostly apply to design criteria on the estimates of regression coefficients.…
In a seminal paper \cite{studden1968} characterized $c$-optimal designs in regression models, where the regression functions form a Chebyshev system. He used these results to determine the optimal design for estimating the individual…
This paper is devoted to the explicit construction of optimal designs for discrimination between two polynomial regression models of degree $n-2$ and $n$. In a fundamental paper, Atkinson and Fedorov [Biometrika 62 (1975a) 57--70] proposed…
In this paper optimal experimental designs for inverse quadratic regression models are determined. We consider two different parameterizations of the model and investigate local optimal designs with respect to the $c$-, $D$- and…
Automated model selection is often proposed to users to choose which machine learning model (or method) to apply to a given regression task. In this paper, we show that combining different regression models can yield better results than…
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…
We propose an algorithm to construct optimal exact designs (EDs). Most of the work in the optimal regression design literature focuses on the approximate design (AD) paradigm due to its desired properties, including the optimality…
Polyhedral estimate is a generic efficiently computable nonlinear in observations routine for recovering unknown signal belonging to a given convex compact set from noisy observation of signal's linear image. Risk analysis and optimal…