-optimal designs for a hierarchically ordered system of regression models

-optimal designs are described for a kind of hierarchically ordered system of regression models with an r-dimensional response variable y. The components of y may be correlated with a known variance-covariance matrix [Sigma]. The present results show that -optimal designs for this system of regression models do not depend on [Sigma]. The -optimal designs are given for the systems of trigonometric and Haar wavelet regression models, respectively.