STRONG REPRESENTATION OF THE QUANTILE FUNCTION FOR LEFT TRUNCATED AND DEPENDENT DATA

Abstract

International audienceLet (X i) i≥1 be a sequence of strong-mixing random variables with common unknown absolutely continuous distribution function F subject to random left truncation. Let F −1 (p) denote the pth (p ∈]0, 1[) quantile function of the marginal distribution function of the X i 's which is estimated by the sample quantile F −1 n (p). In this paper, we derive the strong consistency and a strong representation for F −1 n (p), the quantile function of the Lynden-Bell estimator of F for strong-mixing processes

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