Inference for High-Dimensional Exchangeable Arrays

We consider inference for high-dimensional separately and jointly exchangeable arrays where the dimensions may be much larger than sample sizes. For both arrays, we first derive central limit theorems over rectangles subsequently develop novel multiplier bootstraps with theoretical guarantees. These results rely on new technical tools such as Hoeffding-type decomposition maximal inequalities degenerate components in Hoeffiding-type arrays. exhibit applications of our methods to uniform confidence bands density estimation under joint exchangeability penalty choice l1-penalized regression separate exchangeability. Extensive simulations demonstrate precise coverage rates. illustrate by constructing international trade network densities.