Strong Approximation of Quantile Function for Strong Mixing and Censored Processes

• Published in: Communications in statistics. Theory and methods Vol. 34; no. 7; pp. 1449 - 1459
• Main Authors: Ould-Saïd, Elias, Sadki, Ourida
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 01.07.2005; Taylor & Francis
• Subjects: Bahadur representation; Censored data; Exact sciences and technology; Kaplan-Meier estimator; Mathematics; Nonparametric inference; Probability and statistics; Quantile function; Sciences and techniques of general use; Statistics; Strong consistency; Strong-mixing; Censored data; Mixed distribution; Kaplan Meier estimator; Strong-mixing. 62G05; Strong consistency; Random variable sequence; Random distribution; Statistical method; Censored process; Marginal distribution; Kaplan-Meier estimator; 62G20; Bahadur representation; Quantile; Quantile function
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1081/STA-200063191

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.