Smooth estimate of quantiles under association

Abstract

Let X1,X2,... be real-valued random variables forming a strictly stationary sequence, and satisfying the basic requirement of being positively or negatively associated. Let ξp denote the pth quantile of the marginal distribution function of the Xi's, which is estimated by a smooth (kernel-type) estimate ξ̂pn, on the basis of the segment X1,...,Xn.. The main results of this paper are those of establishing pointwise consistency, asymptotic normality with rates, and weak convergence of a stochastic process generated by ξ̂pn.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1016/s0167-7152(97)00074-6

Keywords

Berry-Esseen bounds, Negative association, Positive association, Smooth estimate, Strict stationarity, Strong consistency, Weak convergence

Publication Date

12-15-1997

Journal Title

Statistics and Probability Letters

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