Inference for High-Dimensional Exchangeable Arrays

Harold D. Chiang, Kengo Kato and Yuya Sasaki

Journal of the American Statistical Association, 2023, vol. 118, issue 543, 1595-1605

Abstract: We consider inference for high-dimensional separately and jointly exchangeable arrays where the dimensions may be much larger than the sample sizes. For both exchangeable arrays, we first derive high-dimensional central limit theorems over the rectangles and subsequently develop novel multiplier bootstraps with theoretical guarantees. 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 exhibit applications of our methods to uniform confidence bands for density estimation under joint exchangeability and penalty choice for l1-penalized regression under separate exchangeability. Extensive simulations demonstrate precise uniform coverage rates. We illustrate by constructing uniform confidence bands for international trade network densities.

Date: 2023
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Working Paper: Inference for high-dimensional exchangeable arrays (2021)
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DOI: 10.1080/01621459.2021.2000868

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