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Higher-order expansions of sample range from general error distribution

Author

Listed:
  • Yingyin Lu
  • Xin Liao
  • Jinhui Guo

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.

Suggested Citation

  • Yingyin Lu & Xin Liao & Jinhui Guo, 2024. "Higher-order expansions of sample range from general error distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(12), pages 4498-4514, June.
  • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:12:p:4498-4514
    DOI: 10.1080/03610926.2023.2184187
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