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Book Chapter

Using a generalized delta-squared-distribution for constructing exact D-optimal designs

Missov, T. I., Ermakov, S. M.

In: Melas, V. B., Mignani, S., Monari, P., Salmaso, L. (Eds.): Topics in statistical simulation: research from the 7th International Workshop on Statistical Simulation, 393-400 (2014)
Springer proceedings in mathematics and statistics 114
New York: Springer.

ISBN 978-1-4939-2103-4, eISBN 978-1-4939-2104-1 , DOI:10.1007/978-1-4939-2104-1_38

Keywords: multivariate analysis, optimization models, probability, simulation, statistics

Abstract

We propose a three-step procedure for exact D-optimal design construction by taking advantage of the structure of the information matrix, whose determinant is to be maximized. First, introducing a simulation procedure for the generalized delta-squared-distribution, we generate samples from the generalized D2. Then, we estimate the resulting modes and run a differential evolution algorithm for precisely allocating the global maximum. The procedure depends neither on the choice of the experimental region, nor on the system of linearly independent functions in it. We present results for polynomial regression in uni- and two-dimensional regions.

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