Higher-order expansions of sample range from general error distribution

Yingyin Lu, Xin Liao and Jinhui Guo

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 12, 4498-4514

Abstract: Let {Xn,n≥1} be a sequence of independent random variables with common general error distribution GED(v) with shape parameter v>0, and denote Mn and mn the partial maximum and minimum of {Xn,n≥1}. With different normalizing constants, the distributional expansions of normalized sample range Mn−mn are established in this article. A byproduct is to deduce the convergence rates of distributions of normalized sample range to their limits, which shows that the optimal convergence rate is proportional to 1/ log n as v∈(0,1)∪(1,∞) contrary to the case of v=1, which is proportional to 1/n. Furthermore, numerical analysis is provided to illustrate the theoretical findings.

Date: 2024
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DOI: 10.1080/03610926.2023.2184187

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