We establish the Bahadur representation of sample quantiles for linear and some widely used nonlinear processes. Local fluctuations of empirical processes are discussed. Applications to the trimmed and Winsorized means are given. Our results extend previous ones by establishing sharper bounds under milder conditions and thus provide new insight into the theory of empirical processes for dependent random variables.
"On the Bahadur representation of sample quantiles for dependent sequences." Ann. Statist. 33 (4) 1934 - 1963, August 2005. https://doi.org/10.1214/009053605000000291