Inference for high-dimensional exchangeable arrays

• Tác giả: Harold D Chiang, Kengo Kato, Yuya Sasaki
• Ngôn ngữ: eng
• Ký hiệu phân loại: 539.76 High-energy physics
• Thông tin xuất bản: 2020
• Bộ sưu tập: Metadata
• ID: 165178

Tóm tắt

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.