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.

翻译：经验似然能够提供一种非参数、基于似然推断的风格，而无需参数模型中常规的严格假设。我们开发了一个将经验似然应用于实验设计分析的框架，解决了区组化和多重假设检验所引发的问题。除了诸如平衡不完全区组设计等常见设计外，我们的方法还适用于高度不平衡的不完全区组设计。我们推导出一组经验似然检验统计量的渐近多元卡方分布，并提出了两种单步多重检验程序：渐近蒙特卡罗法和非参数自助法。这两种程序均能渐近地控制广义族错误率，并在无需显式考虑底层协方差结构的情况下，有效地为感兴趣的比较构建同时置信区间。模拟研究表明，这些程序在违背线性混合模型标准假设时表现稳健。我们还将其应用于一项农药实验。