Empirical likelihood for the analysis of experimental designs

TL;DR

This paper introduces a nonparametric empirical likelihood framework for analyzing various experimental designs, including unbalanced and incomplete blocks, with robust multiple testing procedures and practical applications.

Contribution

It develops a novel empirical likelihood approach tailored for complex experimental designs, addressing blocking, unbalanced data, and multiple hypothesis testing.

Findings

Asymptotic chi-square distribution for test statistics

Procedures control family-wise error rate asymptotically

Robust performance demonstrated in simulation and pesticide experiments

Abstract

Empirical likelihood enables a nonparametric, likelihood-driven style of inference without restrictive assumptions routinely made in parametric models. We develop a framework for applying empirical likelihood to the analysis of experimental designs, addressing issues that arise from blocking and multiple hypothesis testing. In addition to popular designs such as balanced incomplete block designs, our approach allows for highly unbalanced, incomplete block designs. We derive an asymptotic multivariate chi-square distribution for a set of empirical likelihood test statistics and propose two single-step multiple testing procedures: asymptotic Monte Carlo and nonparametric bootstrap. Both procedures asymptotically control the generalised family-wise error rate and efficiently construct simultaneous confidence intervals for comparisons of interest without explicitly considering the underlying covariance structure. A simulation study demonstrates that the performance of the procedures is robust to violations of standard assumptions of linear mixed models. We also present an application to experiments on a pesticide.