We address the problem of estimating quantile-based statistical functionals, when the measured or controlled entities depend on exogenous variables which are not under our control. As a suitable tool we propose the empirical process of the average regression quantiles. It partially masks the effect of covariates and has other properties convenient for applications, e.g. for coherent risk measures of various types in the situations with covariates.

Consider an autoregressive model with measurement error: we observe Zi = Xi + εi, where the unobserved Xi is a stationary solution of the autoregressive equation Xi = gθ0(Xi − 1) + ξi. The regression function gθ0 is known up to a finite dimensional parameter θ0 to be estimated. The distributions of ξ1 and X0 are unknown and gθ belongs to a large class of parametric regression functions. The distribution of ε0is completely known. We propose an estimation procedure with a new criterion computed as...

Dispersion of measurement results is an important parameter that enables us not only to characterize not only accuracy of measurement but enables us also to construct confidence regions and to test statistical hypotheses. In nonlinear regression model the estimator of dispersion is influenced by a curvature of the manifold of the mean value of the observation vector. The aim of the paper is to find the way how to determine a tolerable level of this curvature.

We consider a failure hazard function, conditional on a time-independent covariate Z, given by ${\eta }_{{\gamma }^0}\left(t\right)f_{{\beta }^0}\left(Z\right)$. The baseline hazard function ${\eta }_{{\gamma }^0}$ and the relative risk $f_{{\beta }^0}$ both belong to parametric families with ${\theta }^0={({\beta }^0,{\gamma }^0)}^{\top }\in {ℝ}^{m+p}$. The covariate Z has an unknown density and is measured with an error through an additive error model U = Z + ε where ε is a random variable, independent from Z, with known density $f_{\epsilon }$. We observe a n-sample (Xi, Di, Ui), i = 1, ..., n, where Xi is the minimum between the failure time and the censoring time, and...

Numerical evaluation of the optimal nonlinear robust control requires estimating the impact of parameter uncertainties on the system output. The main goal of the paper is to propose a method for estimating the norm of an output trajectory deviation from the nominal trajectory for nonlinear uncertain, discrete-time systems. The measure of the deviation allows us to evaluate the robustness of any designed controller. The first part of the paper concerns uncertainty modelling for nonlinear systems...