Suppose that one observes a process Y on the unit interval, where dY (t)= n1/2 f (t) dt+ dW (t)
with an unknown function parameter f, given scale parameter n≥ 1 (" sample size") and …

A general framework for estimating nonlinear functions and systems is described and
analyzed in this paper. Identification of a system is seen as estimation of a predictor function …

Identification of nonlinear systems is a multifaceted research area, with many diverse
approaches and methods. This thesis considers two different approaches:(nonparametric) …

Methods of clutter rejection are discussed which furnish an inherent counterpart of target
tracking and detection algorithms. We describe how nonparametric curve estimation …

We consider estimation of a linear functional $ T (f) $ where $ f $ is an unknown function
observed in Gaussian white noise. We find asymptotically sharp adaptive estimators on …

Precise asymptotic descriptions of the minimax affine risks and bias-variance tradeoffs for
estimating linear functionals are given for a broad class of moduli. The results are …

Within the nonparametric regression model with unknown regression function l and
independent, symmetric errors, a new multiscale signed rank statistic is introduced and a …

In this paper, we study the estimation of a function based on noisy inhomogeneous data (the
amount of data can vary on the estimation domain). We consider the model of regression …

This article presents a sequential estimation procedure for an unknown regression function.
Observed regressors and noises of the model are supposed to be dependent and form …

The Appendices contain the proofs of Sections 3, 4, 5 and 6. Moreover, a simulation study is
given together with an exemplified discussion of the connection of tolerant testing in the …