Properties of a covariance matrix with an application to D-optimal design

Abstract

In this paper, a covariance matrix of circulant correlation, R, is studied. A pattern of
entries in R⁻¹ independent of the value ρ of the correlation coefficient is proved based on a recursive relation among the entries of R⁻¹. The D-optimal design for simple linear regression with circulantly correlated observations on [a, b] (a<b) is obtained if even observations are taken and the correlation coefficient is between 0 and 0.5.