This paper deals with a quite general nonparametric statistical curve estimation setting. Special cases include estimation or probability density functions, regression functions, and hazard functions. The class of "fractional delta sequence estimators" is defined and treated here. This class...

Statistics is considered to be a difficult science since it requires a variety of skills including handling of quantitative data, graphical insights as well as mathematical ability. Yet ever increasing special knowledge of statistics is demanded since data of increasing complexity and size need...

For the purpose of comparing different nonparametric density estimators, Wegman (J. Statist. Comput. Simulation 1 225-245) introduced an empirical error criterion. In a recent paper by Hall (Stochastic Process. Appl. 13 11-25) it is shown that this empirical error criterion converges to the mean...

A model is developed for multivariate distributions which have nearly the same marginals, up to shift and scale. This model, based on "interpolation" of characteristic functions, gives a new notion of "correlation". It allows straightforward nonparametric estimation of the common marginal...

The kernel function in density estimation is uniquely determined up to a scale factor. In this paper, we advocate one particular rescaling of a kernel function, called the canonical kernel, because it is the only version which uncouples the problems of choice of kernel and choice of scale...

Kernel density estimators are used for the estimation of integrals of various squared derivatives of a probability density. Rates of convergence in mean squared error are calculated, which show that appropriate values of the smoothing parameter are much smaller than those for ordinary density...