Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 3, Pages 261-267
doi:10.1155/S104895330000023X
Abstract
Let X1,…,Xn be negatively dependent uniformly bounded random
variables with d.f. F(x). In this paper we obtain bounds for the probabilities P(|∑i=1nXi|≥nt) and P(|ξˆpn−ξp|>ϵ) where ξˆpn is the
sample pth quantile and ξp is the pth quantile of F(x). Moreover, we
show that ξˆpn is a strongly consistent estimator of ξp under mild
restrictions on F(x) in the neighborhood of ξp. We also show that ξˆpn
converges completely to ξp.