Inference for High-Dimensional Exchangeable Arrays
Inference for High-Dimensional Exchangeable Arrays
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DOI：
10.1080/01621459.2021.2000868
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发表时间：
2020-09
影响因子：
3.7
通讯作者：
Harold D. Chiang;Kengo Kato;Yuya Sasaki
中科院分区：
文献类型：
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作者：
Harold D. Chiang;Kengo Kato;Yuya Sasaki
摘要我们考虑高维独立和联合可交换阵列的尺寸可能远远大于样本大小的推断。对于这两个可交换的阵列，我们首先推导出高维中心极限定理的矩形，随后开发新的乘法器自举与理论保证。这些理论结果依赖于新的技术工具，如Hoeffding型分解和最大不等式的退化分量的Hoeffding型分解的可交换阵列。我们展示了我们的方法的应用程序，统一的置信带下的联合交换和惩罚的选择下单独的交换下的惩罚回归的密度估计。广泛的模拟表明精确的均匀覆盖率。我们通过构建国际贸易网络密度的统一置信带来说明。
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 -penalized regression under separate exchangeability. Extensive simulations demonstrate precise uniform coverage rates. We illustrate by constructing uniform confidence bands for international trade network densities.