# Multiway empirical likelihood

arXiv: https://arxiv.org/abs/2108.04852 · HTML: https://mlsanity.com/paper/2108.04852/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Aug 2021.

## Built on by (most cited first, 2 of 2)

- [Empirical Likelihood for Random Forests and Ensembles](https://mlsanity.com/paper/2511.13934/) (2025)
- [Cross-Fitting-Free Debiased Machine Learning with Multiway Dependence](https://mlsanity.com/paper/2602.11333/) (2026)

## Abstract (arXiv)

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.