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• 2010-2014  (2)
• English  (2)
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• English  (2)
• 1
Publication Date: 2020-08-05
Description: Let the design of an experiment be represented by an $s$-dimensional vector $\vec{w}$ of weights with non-negative components. Let the quality of $\vec{w}$ for the estimation of the parameters of the statistical model be measured by the criterion of $D$-optimality defined as the $m$-th root of the determinant of the information matrix $M(\vec{w})=\sum_{i=1}^s w_iA_iA_i^T$, where $A_i$, $i=1,...,s$, are known matrices with $m$ rows. In the paper, we show that the criterion of $D$-optimality is second-order cone representable. As a result, the method of second order cone programming can be used to compute an approximate $D$-optimal design with any system of linear constraints on the vector of weights. More importantly, the proposed characterization allows us to compute an \emph{exact} $D$-optimal design, which is possible thanks to high-quality branch-and-cut solvers specialized to solve mixed integer second order cone problems. We prove that some other widely used criteria are also second order cone representable, for instance the criteria of $A$-, and $G$-optimality, as well as the criteria of $D_K$- and $A_K$-optimality, which are extensions of $D$-, and $A$-optimality used in the case when only a specific system of linear combinations of parameters is of interest. We present several numerical examples demonstrating the efficiency and universality of the proposed method. We show that in many cases the mixed integer second order cone programming approach allows us to find a provably optimal exact design, while the standard heuristics systematically miss the optimum.
Language: English
Type: reportzib , doc-type:preprint
Format: application/pdf
Format: application/pdf
Format: application/pdf
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• 2
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Publication Date: 2020-08-05
Description: We consider a stationary discrete-time linear process that can be observed by a finite number of sensors. The experimental design for the observations consists of an allocation of available resources to these sensors. We formalize the problem of selecting a design that maximizes the information matrix of the steady-state of the Kalman filter, with respect to a standard optimality criterion, such as $D-$ or $A-$optimality. This problem generalizes the optimal experimental design problem for a linear regression model with a finite design space and uncorrelated errors. Finally, we show that under natural assumptions, a steady-state optimal design can be computed by semidefinite programming.
Language: English
Type: reportzib , doc-type:preprint
Format: application/pdf
Library Location Call Number Volume/Issue/Year Availability
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