Bootstrapping m " role="presentation"> m m m -generalized order statistics with variable rank

AIMS Mathematics

article

H. M. Barakat¹  Magdy E. El-Adll²  M. E. Sobh³ 

[1] Department of Mathematics, Faculty of Science, Zagazig University;Department of Mathematics, Faculty of Science, Helwan University;Department of Mathematics, Faculty of Science, Mansoura University

关键词: bootstrap method;    consistency;    central order statistics;    intermediate order statistics;    generalized order statistics;   

DOI  :  10.3934/math.2022755

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY