Nonparametric estimation of nonstationary velocity fields from 3D particle tracking velocimetry data is considered. The velocities of tracer particles are computed from their positions measured experimentally with random errors by high-speed cameras observing turbulent flows in fluids. Thus...

Given a sample of a d-dimensional design variable X and observations of the corresponding values of a measurable function m:Rd→R without additional errors, we are interested in estimating m on whole Rd such that the L1 error (with integration with respect to the design measure) of the estimate...

In this paper we study the problem of estimating the density of the error distribution in a random design regression model, where the error is assumed to be independent of the design variable. Our main result is that the L1 error of the kernel density estimate applied to residuals of a...

Estimation of regression functions from independent and identically distributed data is considered. The L2 error with integration with respect to the design measure is used as an error criterion. Usually in the analysis of the rate of convergence of estimates besides smoothness assumptions on...

Given an independent and identically distributed sample of the distribution of an -valued random vector (X,Y), the problem of estimation of the essential supremum of the corresponding regression function is considered. Estimates are constructed, which converge almost surely to this value...

We design a data-dependent metric in Rd and use it to define the k-nearest neighbors of a given point. Our metric is invariant under all affine transformations. We show that, with this metric, the standard k-nearest neighbor regression estimate is asymptotically consistent under the usual...