Strong Approximation of Quantile Function for Strong Mixing and Censored Processes - Ould-Saïd, Elias; Sadki, Ourida (Communications in statistics. Theory and methods, 2005)
Let (X i ) i≥1 be a sequence of strong-mixing random variables with common unknown absolutely continuous distribution function F subject to random right censoring. Let F −1 (p) denote the pth (p ∈ ]0, 1[) quantile function of the marginal distribution function F of the X i ′s which is estimated by a sample quantile (p). In this article, we derive the strong consistency and a Bahadur-type representation for (p), the quantile function of the Kaplan-Meier estimator of F for strong-mixing processes. Then we extend the result of Cheng ( 1984 ) to the dependent case.