The asymptotic properties of a multivariate location estimator are obtained in this paper. The estimator examined is based on the notion of half-space depth, where the depth of a point is the minimum probability content of all half spaces containing the point. The location estimator of interest...

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...