TY  - JOUR
AU  - Barakat, H. M.
AU  - El-Adll, Magdy E.
AU  - Sobh, M. E.
PY  - 2022
TI  - Bootstrapping    m-generalized order statistics with variable rank
JO  - AIMS Mathematics
SP  - 13704
EP  - 13732
VL  - 7
IS  - 8
AB  - 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.
UR  - https://doi.org/10.3934/math.2022755
DO  - 10.3934/math.2022755