A tool for user choice of the local bandwidth function for a kernel density estimate is developed using KDE, a graphical object-oriented package for interactive kernel density estimation written in LISP-STAT. The bandwidth function is a cubic spline, whose knots are manipulated by the user in...

High-dimension, low-small-sample size datasets have different geometrical properties from those of traditional low-dimensional data. In their asymptotic study regarding increasing dimensionality with a fixed sample size, Hall et al. (2005) showed that each data vector is approximately located on...

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...

This paper gives asymptotically best data based choices of the bandwidth of the kernel density estimator. These bandwith selectors attain the fastest possible rate of convergence to the desired theoretical optimum and the best possible constant coefficient in the spirit of the usual Fisher...

In nonparametric kernel regression, most automatically chosen bandwidths are known to have the disturbing property of being negatively correlated with the squared error optimal bandwidth. Fourier analysis method provide insight into the cause of this negative correlation, which is far deeper...

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...