Multiway empirical likelihood

Harold D Chiang; Yukitoshi Matsushita; Taisuke Otsu

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arXiv · 2108.04852

Multiway empirical likelihood

Harold D Chiang·Yukitoshi Matsushita·Taisuke Otsu

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Abstract

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.

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Harold D Chiang, Yukitoshi Matsushita, Taisuke Otsu. 2021-08-10. Multiway empirical likelihood. https://arxiv.org/abs/2108.04852

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