Inference for High-Dimensional Exchangeable Arrays

• 成果类型: Article
• 署名作者: Chiang, Harold D.; Kato, Kengo; Sasaki, Yuya
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; Cornell University; Vanderbilt University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.2000868
• 发表日期: 2023
• 页码: 1595-1605
• 关键词: Gaussian Approximation; LIMIT-THEOREMS; U-statistics; bootstrap; models; regression; selection; suprema; maxima; graphs

摘要

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 l(1)-penalized regression under separate exchangeability. Extensive simulations demonstrate precise uniform coverage rates. We illustrate by constructing uniform confidence bands for international trade network densities.