论文标题
高维交换阵列的推断
Inference for high-dimensional exchangeable arrays
论文作者
论文摘要
我们考虑分别和共同可交换阵列的高维度的推断，其中尺寸可能比样本量大得多。对于两个可交换阵列，我们首先在矩形上得出高维的中心限制定理，并随后使用理论保证开发新颖的乘数引导程序。这些理论上的结果依赖于新的技术工具，例如Hoeffding型分解和最大不平等现象，用于可交换阵列的HoFering-type分解中的退化组件。我们在联合交换性和罚款选择下，在单独的交换性下的$ \ ell_1 $ penalizatizatization回归中，我们在统一的置信频带上展示了我们在统一置信带中的应用。广泛的模拟显示出精确的均匀覆盖率。我们通过为国际贸易网络密度构建统一信心带来说明。
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 $\ell_1$-penalized regression under separate exchangeability. Extensive simulations demonstrate precise uniform coverage rates. We illustrate by constructing uniform confidence bands for international trade network densities.
