Smooth estimate of quantiles under association
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.
Berry-Esseen bounds, Negative association, Positive association, Smooth estimate, Strict stationarity, Strong consistency, Weak convergence
Cai, Zongwu, and George G. Roussas. "Smooth estimate of quantiles under association." Statistics & probability letters 36, no. 3 (1997): 275-287.
Statistics and Probability Letters