Asymptotic optimal designs under long-range dependence error structure

TL;DR

This paper investigates asymptotic optimal experimental designs for regression models with long-range dependence errors, showing they depend indirectly on the correlation function and comparing them with short-range dependence designs.

Contribution

It derives asymptotic optimal designs for models with long-range dependence and compares them to existing short-range dependence designs.

Findings

Optimal designs depend indirectly on the correlation function.

Comparison shows differences between long-range and short-range dependence designs.

Examples illustrate the theoretical results.

Abstract

We discuss the optimal design problem in regression models with long-range dependence error structure. Asymptotic optimal designs are derived and it is demonstrated that these designs depend only indirectly on the correlation function. Several examples are investigated to illustrate the theory. Finally, the optimal designs are compared with asymptotic optimal designs which were derived by Bickel and Herzberg [Ann. Statist. 7 (1979) 77--95] for regression models with short-range dependent error.