Falk, Michael Asymptotic normality of the kernel quantile estimator. (English) Zbl 0567.62035 Ann. Stat. 13, 428-433 (1985). Multidimensional asymptotic normality of the kernel quantile estimator is established under fairly general conditions on the underlying distribution function and on the kernel. Sharpening these assumptions, one can utilize the proof to achieve also a bound for the rate of convergence which entails the comparison of the kernel estimator with the empirical quantile on the basis of their covering probabilities. Cited in 2 ReviewsCited in 49 Documents MSC: 62G05 Nonparametric estimation 60F05 Central limit and other weak theorems 62E20 Asymptotic distribution theory in statistics Keywords:central limit theorem; Multidimensional asymptotic normality; kernel quantile estimator; bound for the rate of convergence; empirical quantile; covering probabilities PDFBibTeX XMLCite \textit{M. Falk}, Ann. Stat. 13, 428--433 (1985; Zbl 0567.62035) Full Text: DOI