Asymptotic behavior of bootstrapped lower extreme generalized order statistics under linear normalization

Abstract This paper investigates the bootstrap behavior of linearly normalized lower extreme m -generalized order statistics ( m -GOSs). We derive sharp conditions for inconsistency, weak consistency, and strong consistency of the bootstrap procedure. Our results refine those of Barakat et al. (“Bootstrap for extreme generalized order statistics,” Arabian J. Sci. Eng. , vol. 36, no. 6, pp. 1083–1090, 2011) by showing that the full-sample bootstrap is inconsistent for all m ≥ 0. In addition, simulation results identify resample sizes that minimize divergence from the target distribution, improving the accuracy of bootstrap approximations.