An estimator of a smooth quantile function (q.f.) is constructed by Bernstein polynomial smoothing of the empirical quantile function. Asymptotic behavior of this estimator is demonstrated by a weighted Brownian bridge in-probability uniform approximation. Oscillation behavior of this estimator...

A Berry-Esséen-type theorem showing the near-optimal quality of the normal distribution approximation to the distribution of smooth quantile density estimators is established in this paper. Under more restrictive conditions on the smoothing kernel, an n-1/2-error bound Berry-Esséen result is...

Based on a careful analysis of the asymptotic almost-sure behavior of certain generalized Kiefer processes, asymptotic almost-sure uniform upper bounds of estimation error are established for a broad class of quantile density function estimators useful in survival analysis. The error bounds are...

A concept called concentration order of probability distributions on a metric space is introduced, then the norm stochastic order that compares real-parameter stochastic processes is introduced as a special case. Equivalent conditions of concentration order are established. Using Anderson's...