D-optimal designs for the Mitscherlich non-linear regression function

TL;DR

This paper develops D-optimal experimental designs for the Mitscherlich non-linear regression model applicable to various response distributions within the exponential family, extending beyond the traditional normal response case.

Contribution

It introduces a method to construct D-optimal designs for Mitscherlich's function with responses from the exponential family, linking to weighted linear regression.

Findings

D-optimal designs for exponential family responses are derived.

Connections established between non-linear and weighted linear regression optimality.

Designs improve efficiency for a broader class of response distributions.

Abstract

Mitscherlich's function is a well-known three-parameter non-linear regression function that quantifies the relation between a stimulus or a time variable and a response. Optimal designs for this function have been constructed only for normally distributed responses with homoscedastic variances. In this paper, we construct D-optimal designs for discrete and continuous responses having their distribution function in the exponential family. We also demonstrate the connection with D-optimality for weighted linear regression.