## JMI2012A-3 An algorithm for calculating $D$-optimal designs for trigonometric regression through given points in terms of the discrete modified KdV equation (pp.17-23)

Author(s)： Hiroto Sekido

J. Math-for-Ind. 4A (2012) 17-23.

Abstract
Optimal designs are required to make efficient statistical experiments. Calculation of $D$-optimal designs is considerably simplified by using canonical moments or trigonometric canonical moments. On the other hand, integrable systems are dynamical systems whose solutions can be written down concretely. In the previous paper, Sekido 2011, a method for calculating $D$-optimal designs for polynomial regression through a fix point is presented. In this paper, trigonometric regression models through given points are discussed. In order to calculate the $D$-optimal designs for these models, a useful relationship between trigonometric canonical moments and a class of discrete integrable systems is found. By using trigonometric canonical moments and a discrete integrable system, a new algorithm for calculating $D$-optimal designs for these models is proposed.

Keyword(s).　 $D$-optimal design, trigonometric canonical moment, trigonometric regression model, integrable system, discrete modified Korteweg-de Vries equation