This paper derives new maximal inequalities for empirical processes associated with separately exchangeable (SE) random arrays. For any fixed index dimension \(K\ge 1\), we establish a global maximal inequality that bounds the \(q\)-th moment, for any \(q\in[1,\infty)\), of the supremum of these processes. In addition, we obtain a refined local maximal inequality that controls the first absolute moment of the supremum. Both results are proved for a general pointwise measurable class of functions.

翻译：本文推导了与可分离可交换随机阵列相关的经验过程的新最大不等式。对于任意固定的指标维度 \(K\ge 1\)，我们建立了一个全局最大不等式，该不等式界定了这些过程上确界的任意 \(q\in[1,\infty)\) 阶矩。此外，我们获得了一个精细的局部最大不等式，用于控制上确界的一阶绝对矩。这两个结果都是针对一类一般的逐点可测函数类证明的。