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, two-stage sampling, generalized estimating equations, and three-way observations.
翻译:本文为多组实体编制索引的观测制定了统计推论的一般方法。 我们提出一种新的多路实验概率统计,在非变性情况下,与相对应的Hoffding型分解以线性术语为主的奇平方分布相融合。 我们的方法与jacknife经验可能性的概念有关,但假冒值则通过留下列或行来构建。 我们进一步开发了我们多路实验概率统计的修改版本,它与奇平方分布相融合,而不论退化程度如何,并发现与传统的Eicker-White型差异估计仪的t-ratio相比,其可取的较高顺序属性。 拟议的方法通过几个重要的统计问题来说明,如双方网络、两阶段抽样、通用估计方程和三道观察。