This paper develops a general methodology to conduct statistical inference for observations indexed by multiple sets of entities. We propose a novel multiway empirical likelihood statistic that converges to a chi-square distribution under the non-degenerate case, where corresponding Hoeffding type decomposition is dominated by linear terms. Our methodology is related to the notion of jackknife empirical likelihood but the leave-out pseudo values are constructed by leaving columns or rows. We further develop a modified version of our multiway empirical likelihood statistic, which converges to a chi-square distribution regardless of the degeneracy, and discover its desirable higher-order property compared to the t-ratio by the conventional Eicker-White type variance estimator. The proposed methodology is illustrated by several important statistical problems, such as bipartite network, generalized estimating equations, and three-way observations.

翻译：本文提出了一种针对多组实体索引观测数据进行统计推断的通用方法。我们构建了一种新颖的多路经验似然统计量，在非退化情形下（此时对应的Hoeffding型分解由线性项主导），该统计量收敛于卡方分布。该方法与折刀经验似然概念相关，但留出伪值是通过剔除行或列的方式构造的。我们进一步改进了多路经验似然统计量的修正版本——无论退化情形如何均能收敛于卡方分布，并发现相较于传统Eicker-White型方差估计量下的t统计量，该修正版本具有更优的高阶性质。本文通过二分网络、广义估计方程以及三路观测等若干重要统计问题对所提方法进行了验证。