AIMS Mathematics (May 2022)

Bootstrapping m-generalized order statistics with variable rank

  • H. M. Barakat,
  • Magdy E. El-Adll,
  • M. E. Sobh

DOI
https://doi.org/10.3934/math.2022755
Journal volume & issue
Vol. 7, no. 8
pp. 13704 – 13732

Abstract

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In this paper, several bootstrap properties of m-generalized order statistics (m-GOSs) with variable rank (central and intermediate) are revealed. We study the inconsistency, weak consistency and strong consistency of bootstrapping central and intermediate m-GOSs when the normalizing constants are assumed to be known or estimated from the re-sampled data using a proper re-sample size. Furthermore, sufficient conditions for the weak and strong consistencies of the bootstrapping distributions of central and intermediate m-GOSs based on the normalizing constant estimators are given. Finally, a simulation study is conducted to determine the optimal bootstrap re-sample size corresponding to the best fitting of the bootstrapping distribution.

Keywords