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.

翻译：本文推导了与可分离可交换随机阵列相关联的经验过程的新最大不等式。对于固定指标维度 $K\ge 1$，我们建立了一个全局最大不等式，用于界定这些过程上确界的 $q$ 阶矩（$q\in[1,\infty)$）。我们还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。两个结果均针对一般的逐点可测函数类进行证明。我们的方法采用了一种新技术，将指标集划分为横向组，从而解耦依赖性并实现更复杂的高阶矩界。