Inference for High-Dimensional Exchangeable Arrays

We consider inference for high-dimensional exchangeable arrays where the dimension may be much larger than the cluster sizes. Specifically, we consider separately and jointly exchangeable arrays that correspond to multiway clustered and polyadic data, respectively. Such exchangeable arrays have seen a surge of applications in empirical economics. However, both exchangeability concepts induce highly complicated dependence structures, which poses a significant challenge for inference in high dimensions. In this paper, we first derive high-dimensional central limit theorems (CLTs) over the rectangles for the exchangeable arrays. Building on the high-dimensional CLTs, we develop novel multiplier bootstraps for the exchangeable arrays and derive their finite sample error bounds in high dimensions. The derivations of these theoretical results rely on new technical tools such as Hoeffding-type decomposition and maximal inequalities for the degenerate components in the Hoeffiding-type decomposition for the exchangeable arrays. We illustrate applications of our bootstrap methods to robust inference in demand analysis, robust inference in extended gravity analysis, and penalty choice for $\ell_1$-penalized regression under multiway cluster sampling.