A Bahadur-Type Representation for Empirical Quantiles of a Large Class of Stationary, Possibly Infinite-Variance, Linear Processes

On the Bahadur representation of sample quantiles for dependent sequences

“…Assuming that E(|ε k | α ) < ∞ for some α > 0 and that |a n | = O(n −κ ) with κ > 1 + 2/α, Hesse [16] obtained the representation…”

“…Extensions of the above results to dependent random variables have been pursued in [26] for m-dependent processes, in [27] for strongly mixing processes, in [16] for short-range dependent (SRD) linear processes and in [17] for long-range dependent (LRD) linear processes. The main objective of this paper is to generalize and refine these results for linear and some nonlinear processes.…”

Bahadur representation for U-quantiles of dependent data

“…Babu and Singh [3] proved such a representation under an exponentially fast decay of the strong mixing coefficients, this was weakened by Yoshihara [37] and Sun [33] to a polynomial decay of the strong mixing coefficients. Hesse [16], Wu [35] and Kulik [23] established a Bahadur representation for linear processes. The first aim of this paper is to give better rates than Sun under polynomial strong mixing.…”

Nonparametric estimation of quantiles for a class of stationary processes

“…As a nonparametric method, the sample quantile has the advantages of being free of distribution assumptions on the random variables, while being able to capture the situations of fattail distribution automatically, and was widely researched and used in the last decades. For example, Serfling [12] discussed its asymptotic theory in great details, and some recent contributions on this area can be found among Hesse [6], Wu [15], Kulik [8] and so on.…”