Based on a random sample of size n from an unknown d-dimensional density f, the problem of selecting the variable (or adaptive) bandwidth in kernel estimation of f is investigated. The common strategy is to express the variable bandwidth at each observation as the product of a local bandwidth...

Mode estimation is an important task, because it has applications to data from a wide variety of sources. Many mode estimates have been proposed with most based on nonparametric density estimates. However, mode estimates obtained by such methods, although they perform excellently with large...

An Lp, 1 [less-than-or-equals, slant] p [less-than-or-equals, slant] [infinity], nonuniform central limit order bound O(N-1/2) for simple linear rank statistics is obtained. The theorem is proved for a wide class of scores including the van der Waerden scores and the Wilcoxon scores. It extends...

Let be a sequence of independent nonnegative r.v.'s (random variables) with finite second moments. It is shown that under a Lindeberg-type condition, the [alpha]th inverse moment E{a+Xn}-[alpha] can be asymptotically approximated by the inverse of the [alpha]th moment {a+EXn}-[alpha] where , and...

We propose a consistent criterion for model order selection in the model identification phase of time series and regression, based on a weighted average of an asymptotically efficient selection criterion, AICC (bias-corrected Akaike information criterion) and a consistent selection criterion,...