We study the problem of estimating conditional distribution functions from data containing additional errors. The only assumption on these errors is that a weighted sum of the absolute errors tends to zero with probability one for sample size tending to infinity. We prove sufficient conditions...

The problem of the estimation of a regression function by continuous piecewise linear functions is formulated as a nonconvex, nonsmooth optimization problem. Estimates are defined by minimization of the empirical L 2 risk over a class of functions, which are defined as maxima of minima of linear...

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...

A simulation model with outcome Y=m(X) is considered, where X is an Rd-valued random variable and m:Rd→R is p-times continuously differentiable. It is shown that an importance sampling Robbins–Monro type quantile estimate achieves for 0p≤d the rate of convergence...

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...