arXiv subjects

Radoslav Harman

Publications and source records attributed to Radoslav Harman.

22 records · Page 2Linked to original sources

arXiv2015

Optimal approximate designs for estimating treatment contrasts resistant to nuisance effects

Suppose that we intend to perform an experiment consisting of a set of independent trials. The mean value of the response of each trial is assumed to be equal to the sum of the effect of the treatment selected for the trial, and some nuisance effects, e.g., the effect of a time trend, or blocking. In this model, we examine optimal approximate designs for the estimation of a system of treatment contrasts, with respect to a wide range of optimality criteria. We show that it is necessary for any optimal design to attain the optimal treatment proportions, which may be obtained from the marginal model that excludes the nuisance effects. Moreover, we prove that for a design to be optimal, it is sufficient that it attains the optimal treatment proportions and satisfies conditions of resistance to nuisance effects. For selected natural choices of treatment contrasts and optimality criteria, we calculate the optimal treatment proportions and give an explicit form of optimal designs. In particular, we obtain optimal treatment proportions for comparison of a set of new treatments with a set of controls. The results allow us to construct a method of calculating optimal approximate designs with a small support by means of linear programming. As a consequence, we can construct efficient exact designs by a simple heuristic.

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arXiv2014

Approximate D-optimal Experimental Design with Simultaneous Size and Cost Constraints

Consider an experiment with a finite set of design points representing permissible trial conditions. Suppose that each trial is associated with a cost that depends on the selected design point. In this paper, we study the problem of constructing an approximate D-optimal experimental design with simultaneous restrictions on the size and on the total cost. For the problem of size-and-cost constrained D-optimality, we formulate an equivalence theorem and rules for the removal of redundant design points. We also propose a simple monotonically convergent "barycentric" algorithm that allows us to numerically compute a size-and-cost constrained approximate D-optimal design.

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arXiv2014

Heuristic construction of exact experimental designs under multiple resource constraints

The aim of this paper is twofold. First, we introduce "resource constraints" as a general concept that covers many practical restrictions on experimental design. Second, for computing efficient exact designs of experiments under any combination of resource constraints, we propose a tabu search heuristic that uses some ideas of the Detmax procedure. To illustrate the scope and performance of our heuristic, we computed D-efficient designs for 1) a block model with limits on the numbers of blocks and on the availability of experimental material; 2) a quadratic regression model with simultaneous marginal and cost constraints; 3) a non-linear regression model with simultaneous direct and cost constraints. As we show, the proposed heuristic generates comparable or better results than algorithms specialized for computing optimal designs under less general constraints.

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arXiv2007

Improvements on removing non-optimal support points in D-optimum design algorithms

We improve the inequality used in Pronzato [2003. Removing non-optimal support points in D-optimum design algorithms. Statist. Probab. Lett. 63, 223-228] to remove points from the design space during the search for a $D$-optimum design. Let $ξ$ be any design on a compact space $\mathcal{X} \subset \mathbb{R}^m$ with a nonsingular information matrix, and let $m+ε$ be the maximum of the variance function $d(ξ,\mathbf{x})$ over all $\mathbf{x} \in \mathcal{X}$. We prove that any support point $\mathbf{x}_{*}$ of a $D$-optimum design on $\mathcal{X}$ must satisfy the inequality $d(ξ,\mathbf{x}_{*}) \geq m(1+ε/2-\sqrt{ε(4+ε-4/m)}/2)$. We show that this new lower bound on $d(ξ,\mathbf{x}_{*})$ is, in a sense, the best possible, and how it can be used to accelerate algorithms for $D$-optimum design.

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