Due to the complexity of order statistics, the finite sample behaviour of robust statistics is generally not analytically solvable. While the Monte Carlo method can provide approximate solutions, its convergence rate is typically very slow, making the computational cost to achieve the desired accuracy unaffordable for ordinary users. In this paper, we propose an approach analogous to the Fourier transformation to decompose the finite sample structure of the uniform distribution. By obtaining sets of sequences that are consistent with parametric distributions for the first four sample moments, we can approximate the finite sample behavior of other estimators with significantly reduced computational costs. This article reveals the underlying structure of randomness and presents a novel approach to integrate multiple assumptions.

翻译：由于次序统计量的复杂性，稳健统计量的有限样本行为通常无法通过解析方法求解。尽管蒙特卡洛方法能提供近似解，但其收敛速度通常极慢，使得普通用户难以承担达到预期精度所需的计算成本。本文提出一种类似于傅里叶变换的方法，对均匀分布的有限样本结构进行分解。通过获取与参数分布前四阶样本矩一致的序列集合，我们得以显著降低计算成本来近似其他估计量的有限样本行为。本文揭示了随机性的内在结构，并提出了一种整合多重假设的新方法。