Statistica Sinica 12(2002), 1015-1026

$L_p$-OPTIMALITY FOR REGRESSION DESIGNS

UNDER CORRELATIONS

Kim-Hung Li and Nai N. Chan

The Chinese University of Hong Kong and University of Melbourne

Abstract: The input energy constraints in a linear dynamic system considered in this paper are of the form that the Euclidean norm of each column of its design matrix is bounded above by a constant. An exact $L_p$-optimal design is obtained in closed form which is easily computable. Interestingly, the $L_p$-optimal designs for the generalized and the ordinary least squares estimators coincide. An example is given to demonstrate how the results can be used to find a design that performs well under all $L_p$ criteria.

Key words and phrases: CL vector, correlated error, dynamic systems, generalized least squares, Lp-optimal design, majorization, ordinary least squares.