Maximal Inequalities for Separately Exchangeable Empirical Processes

• Tác giả: Harold D Chiang
• Ngôn ngữ: eng
• Ký hiệu phân loại: 612.022 Control processes
• Thông tin xuất bản: 2025
• Bộ sưu tập: Báo, Tạp chí
• ID: 223725

Tóm tắt

This paper derives new maximal inequalities for empirical processes associated with separately exchangeable random arrays. For fixed index dimension $K\ge 1$, we establish a global maximal inequality bounding the $q$-th moment ($q\in[1,\infty)$) of the supremum of these processes. We also obtain a refined local maximal inequality controlling the first absolute moment of the supremum. Both results are proved for a general pointwise measurable function class. Our approach uses a new technique partitioning the index set into transversal groups, decoupling dependencies and enabling more sophisticated higher moment bounds.