Some convergence results for kernel-type quantile estimators under censoring (Q1085916)

In continuation of the investigations of the authors and \textit{K. F. Yu} reviewed above, Zbl 0608.62048, the authors use some strong results on the product-limit estimator and its quantile function, provided by various authors to derive the following: i) Asymptotic normality of \(\sqrt{n}(Q_ n(p)-F^{-1}(p))\), as above, but for arbitrary null-sequence \(h_ n.\) ii) Rates of convergence of \(Q_ n(p)-Q_ n^*(p)\) w.r. to \(L_ 1\) and \(L_ 2\) norms. iii) \(E(Q_ n(p)-F^{-1}(p))^ 2=O(h_ n+h_ n^{1/2}n^{- 5/4}+((\log n)/n)^{3/4})\), as \(n\to \infty\), provided some assumptions on F,K and \(h_ n\) are satisfied.