A note on optimal designs for estimating the slope of a polynomial regression

TL;DR

This paper investigates optimal experimental designs for estimating the slope in polynomial regression without intercept, focusing on asymmetric design spaces and identifying conditions for explicit solutions at specific points.

Contribution

It extends previous symmetric design analyses to asymmetric intervals and characterizes when explicit optimal designs can be derived.

Findings

Identifies conditions for explicit optimal designs at specific points

Analyzes polynomial regression on asymmetric intervals

Provides characterization of optimal design solutions

Abstract

In this note we consider the optimal design problem for estimating the slope of a polynomial regression with no intercept at a given point, say z. In contrast to previous work, which considers symmetric design spaces we investigate the model on the interval $[0, a]$ and characterize those values of $z$, where an explicit solution of the optimal design is possible.