Based on a random sample of size <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>n</mi> </math> </EquationSource> </InlineEquation> from an unknown <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$d$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>d</mi> </math> </EquationSource> </InlineEquation>-dimensional density <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$f$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>f</mi> </math> </EquationSource> </InlineEquation>, the nonparametric estimations of a single integrated density partial derivative functional as well as a vector of such functionals are considered. These single and vector functionals...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

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,...

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...

Due to the advances in computer technology a lot of industrial, biological, and medical processes are continuously monitored by instruments under the control of microprocessors. Thus, our data is a set of curves defined on certain time intervals, i.e., sample paths of continuous-time stochastic...

Industrial processes may be continuously monitored by instruments under control of microprocessors. Thus the data are usually obtained in the form of sets of (continuous) curves over certain time intervals. This paper presents a method of estimating regression parameters in terms of the sample...