Asymptotic properties of sample quantiles constructed from samples with random sizes (Q2711129)

The author provides necessary and sufficient conditions for weak convergence of the joint distribution of sample quantiles constructed from i.i.d. samples \(X_1,\dots, X_{N_n}\) of random sample size \(N_n\). The limit distribution is a mixture of multivariate normal distributions, \(N(0,U^{-1} \Sigma)\), where \(U\) is the weak limit of \(N_n/n\) and \(\Sigma\) is the limiting covariance matrix for sample quantiles with deterministic sample size \(n\). This paper improves on previous research by the author [ibid. 40, No. 4, 770-772 (1995; Zbl 0863.60022); J. Math. Sci., New York 76, No. 2, 2259-2268 (1995; Zbl 0859.60021)].