Before revision:  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.
After revision:  In this paper, we first derive high-dimensional central limit theorems (CLTs) over the rectangles and subsequently develop novel multiplier bootstraps for the exchangeable arrays and derive their finite sample error bounds in high dimensions.