This paper discusses a universal approach to the construction of confidence regions for level sets {h(x)≥0}⊂Rq of a function h of interest. The proposed construction is based on a plug-in estimate of the level sets using an appropriate estimate ĥn of h. The approach provides finite sample...

One of the most difficult problems in applications of semi-parametric partially linear single-index models (PLSIM) is the choice of pilot estimators and complexity parameters which may result in radically different estimators. Pilot estimators are often assumed to be root-n consistent, although...

Let (X1, Y1),..., (Xn, Yn) be i.i.d. rv's and let m(x) = E(YX = x) be the regression curve of Y on X. A M-smoother mn(x) is a robust, nonlinear estimator of m(x), defined in analogy to robust M-estimators of location. In this paper the asymptotic maximal deviation sup0 = t = 1 mn(t) - m(t) is...

Semiparametric single-index regression involves an unknown finite-dimensional parameter and an unknown (link) function. We consider estimation of the parameter via the pseudo-maximum likelihood method. For this purpose we estimate the conditional density of the response given a candidate index...

A robust estimator of the regression function is proposed combining kernel methods as introduced for density estimation and robust location estimation techniques. Weak and strong consistency and asymptotic normality are shown under mild conditions on the kernel sequence. The asymptotic variance...

Discrete versions of the mean integrated squared error (MISE) provide stochastic measures of accuracy to compare different estimators of regression fuctions. These measures of accuracy have been used in Monte Carlo trials and have been employed for the optimal bandwidth selection for kernel...

This paper deals with a quite general nonparametric statistical curve estimation setting. Special cases include estimation or probability density functions, regression functions, and hazard functions. The class of "fractional delta sequence estimators" is defined and treated here. This class...