Optimal designs for comparing regression models with correlated observations

TL;DR

This paper develops optimal experimental designs for comparing two regression models with correlated data, minimizing confidence band width and extending existing methods to dependent observations.

Contribution

It introduces a new approach to construct efficient estimators and designs for correlated data, improving comparison accuracy of regression models.

Findings

Optimal designs reduce confidence band width

Constructed estimators are efficient and unbiased

Numerical examples demonstrate improved comparison performance

Abstract

We consider the problem of efficient statistical inference for comparing two regression curves estimated from two samples of dependent measurements. Based on a representation of the best pair of linear unbiased estimators in continuous time models as a stochastic integral, an efficient pair of linear unbiased estimators with corresponding optimal designs for finite sample size is constructed. This pair minimises the width of the confidence band for the difference between the estimated curves. We thus extend results readily available in the literature to the case of correlated observations and provide an easily implementable and efficient solution. The advantages of using such pairs of estimators with corresponding optimal designs for the comparison of regression models are illustrated via numerical examples.