Some overview on unbiased interpolation and extrapolation designs

TL;DR

This paper explores the theory behind unbiased interpolation and extrapolation designs, linking uniform approximation of functions with optimal design construction, and discusses applications including accelerated testing and multivariate cases.

Contribution

It provides a comprehensive overview connecting uniform approximation theory with the construction of optimal unbiased designs, including multivariate and application-specific insights.

Findings

Established connections between uniform approximation and design optimality

Extended the theory to multivariate cases in specific situations

Presented applications to accelerated testing scenarios

Abstract

This paper considers the construction of optimal designs due to Hoel and Levine and Guest. It focuses on the relation between the theory of the uniform approximation of functions and the optimality of the designs. Some application to accelerated tests is also presented. The multivariate case is also handled in some special situations.