Robust estimations from distribution structures: V. Non-asymptotic

Due to the complexity of order statistics, the finite sample bias 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 a set of sequences that are simultaneously consistent with a parametric distribution for the first four sample moments, we can approximate the finite sample behavior of robust estimators with significantly reduced computational costs. This article reveals the underlying structure of randomness and presents a novel approach to integrate two or more assumptions.