It can be found that widely orthant dependent (WOD) random variables are
weaker than extended negatively orthant dependent (END) random variables,
while END random variables are weaker than negatively orthant dependent (NOD)
and negatively associated (NA) random variables. In this paper, we
investigate the Bahadur representation of sample quantiles based on WOD
sequences. Our results extend the corresponding ones of Ling [N.X. Ling, The
Bahadur representation for sample quantiles under negatively associated
sequence, Statistics and Probability Letters 78(16) (2008), 2660-2663], Xu et
al. [S.F. Xu, L. Ge, Y. Miao, On the Bahadur representation of sample
quantiles and order statistics for NA sequences, Journal of the Korean
Statistical Society 42(1) (2013), 1-7] and Li et al. [X.Q. Li, W.Z. Yang,
S.H. Hu, X.J. Wang, The Bahadur representation for sample quantile under NOD
sequence, Journal of Nonparametric Statistics 23(1) (2011), 59-65] for the
case of NA sequences or NOD sequences.
On the Bahadur representation of sample quantiles for widely orthant dependent sequences