Let X1, ..., Xn be independent identically distributed observations from an unknown probability density f(·), such that its support G = supp f is a subset of the unit square in 2. We consider the problem of estimating G from the sample X1, ..., Xn, under the assumption that the boundary of G...

The problem of optimal prediction in the stochastic linear regression model with infinitely many parameters is considered. We suggest a prediction method that outperforms asymptotically the ordinary least squares predictor. Moreover, if the random errors are Gaussian, the method is...

In this paper bootstrap confidence bands are constructed for nonparametric quantile estimates of regression functions, where resampling is done from a suitably estimated empirical distribution function (edf) for residuals. It is known that the approximation error for the confidence band by the...

We consider a difference based ridge regression estimator and a Liu type estimator of the regression parameters in the partial linear semiparametric regression model, y=Xβ+f+ε. Both estimators are analyzed and compared in the sense of mean-squared error. We consider the case of independent...

This study considers the theoretical bootstrap “coupling” techniques for nonparametric robust smoothers and quantile regression, and we verify the bootstrap improvement. To handle the curse of dimensionality, a variant of “coupling” bootstrap techniques is developed for additive models...

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...