2022/11/08 by Xiao Fang, Fang, Xiao, Songhao Liu +1
Mathematics · #Advanced Mathematical Identities #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Statistical Distribution Estimation and Applications
paper · pdf · doi:10.48550/arxiv.2211.04174
openalex publication_date 2022/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Edgeworth expansion provides higher-order corrections to the normal approximation for a probability distribution. The classical proof of Edgeworth expansion is via characteristic functions. As a powerful method for distributional approximations, Stein's method has also been used to prove Edgeworth expansion results. However, these results assume that either the test function is smooth (which excludes indicator functions of the half line) or that the random variables are continuous (which excludes random variables having only a continuous component). Thus, how to recover the classical Edgeworth expansion result using Stein's method has remained an open problem. In this paper, we develop Stein's method for two-term Edgeworth expansions in a general case. Our approach involves repeated use of Stein equations, Stein identities via Stein kernels, and a replacement argument.