# Locally optimal designs for generalized linear models within the family of Kiefer $\Phi_k$-criteria

## TL;DR

This paper develops analytic solutions for locally optimal experimental designs in generalized linear models using Kiefer $\

## Contribution

It introduces a general framework for deriving analytic locally optimal designs under Kiefer $\

## Key findings

- Analytic solutions for D- and A-optimal designs are provided.
- Necessary and sufficient conditions for optimality are established.
- Designs are characterized via intensity values using the General Equivalence Theorem.

## Abstract

Locally optimal designs for generalized linear models are derived at certain values of the regression parameters. In the present paper a general setup of the generalized linear model is considered. Analytic solutions for optimal designs are developed under Kiefer $\Phi_k$-criteria highlighting the D- and A-optimal designs. By means of The General Equivalence Theorem necessary and sufficient conditions in term of intensity values are obtained to characterize the locally optimal designs. In this context, linear predictors are assumed constituting first order models with and without intercept on appropriate experimental regions.