Before revision: 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 arraysthat 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.
After revision: We consider inference for high-dimensional exchangeable arrays where the dimension may be much larger than the sample sizes. For both exchangeable arrays, we first derive high-dimensional central limit theorems (CLTs) over the rectangles for the exchangeable arrays.