The known asymptotically efficient estimates of a nonlinear functional of an unknown function are crucially depended on prior information about a smoothness of this function. We show on example of filtering that this information is not necessary at all whenever the asymptotically efficient...

In a controlled random design experiment it is often desirable to estimate an underlying regression function with assigned risk, then the optimality is understood as a minimal mean sample size. For the first time in the literature, it is proved that such a sequential procedure exists. Further,...

In a non-parametric regression, the heteroscedasticity (dependence of the variance of the regression error on the predictor) can be a serious complication in estimation or visualization of an underlying regression function. If a controlled sampling is permitted, then the statistician can choose...

The fact that signal-in-noise filtering model can serve as a prototype for nonparametric regression is well known and it is widely used in the nonparametric curve estimation theory. So far the only known examples showing that the equivalence may not hold have been about homoscedastic regressions...