×

Asymptotic normality of the kernel quantile estimator. (English) Zbl 0567.62035

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.

MSC:

62G05 Nonparametric estimation
60F05 Central limit and other weak theorems
62E20 Asymptotic distribution theory in statistics
PDFBibTeX XMLCite
Full Text: DOI