@article{Barakat2022, 
author = {H. M. Barakat and Magdy E. El-Adll and M. E. Sobh},
title = {Bootstrapping    m-generalized order statistics with variable rank},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {8},
pages = {13704-13732},
keywords = {bootstrap method, consistency, central order statistics, intermediate order statistics, generalized order statistics},
url = {https://www.sciopen.com/article/10.3934/math.2022755},
doi = {10.3934/math.2022755},
abstract = {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.}
}