Optimal Design Measures under Asymmetric Errors, with Application to Binary Design Points

TL;DR

This paper develops a theoretical framework for optimal experimental design under asymmetric error distributions using second-order least squares estimation, with specific focus on binary design points and support size reduction.

Contribution

It introduces a general approximate theory for optimal design under asymmetric errors and derives conditions for D- and A-optimal designs, especially for binary design points.

Findings

Necessary and sufficient conditions for optimal design measures.

Application of theory to binary design points.

Addressing support size reduction of optimal designs.

Abstract

We study the optimal design problem under second-order least squares estimation which is known to outperform ordinary least squares estimation when the error distribution is asymmetric. First, a general approximate theory is developed, taking due cognizance of the nonlinearity of the underlying information matrix in the design measure. This yields necessary and sufficient conditions that a D- or A-optimal design measure must satisfy. The results are then applied to find optimal design measures when the design points are binary. The issue of reducing the support size of the optimal design measure is also addressed.