Design for Linear Regression Models with Correlated Errors

The present chapter provides a survey of results on experimental design for linear regression models with correlated responses.

6.1.1 Introduction

The common linear regression model is given by

y(x) = θ1f1(x) + · · · + θmfm(x) + ε(x), (6.1)

where f1(x), . . . , fm(x) are given linearly independent functions, ε(x)denotes a randomerror process or field with E[ε(x)] = 0, x is the explanatory variable, which varies in the design space X ⊂ Rd, and θ1, . . . ,θm are unknown parameters.