In this work, we introduce a smoothed influence function that constitute a theoretical tool for studying the outliers robustness properties of a large class of nonparametric estimators. With this tool, we first show the nonrobustness of the Nadaraya-Watson estimator of regression. Then we show...

We propose a new estimator for nonparametric regression based on local likelihood estimation using an estimated error score function obtained from the residuals of a preliminary nonparametric regression. We show that our estimator is asymptotically equivalent to the infeasible local maximum...

We consider a problem of estimation of parametric components in a partial linear model. Suppose that a finite set E of linear estimators is given. Our goal is to mimic the estimator in E that has the smallest risk. Using a second order expansion of the risk of linear estimators we propose a...

We consider an additive model with second order interaction terms. It is shown how the components of this model can be estimated using marginal integration, and the asymptotic distribution of the estimators is derived. Moreover, two test statistics for testing the presence of interactions are...

This methodological paper discusses the application of "adaptive" non-parametric procedures for estimating regression functions or contrasts in situations with quantitative regressands and qualitative regressors. We propose to apply an adaptive regressogram, that is the selection of a...

A recipe is provided for producing, from a sequence of procedures in the Gaussian regression model, an asymptotically equivalent sequence in the density estimation model with i. i. d. observations. The recipe is, to put it roughly, to calculate square roots of normalised frequencies over certain...

This paper proposes a nonparametric test of the non-convexity of a smooth regression function based on least squares or hybrid splines. By a simple formulation of the convexity hypothesis in the class of all polynomial cubic splines, we build a test which has an asymptotic size equal to the...

Models are studied where the response Y and covariates X, T are assumed to fulfill E(Y|X; T) = G{XT β + α + m1(T1) + … + md(Td)}. Here G is a known (link) function, β is an unknown parameter, and m1, …, md are unknown functions. In particular, we consider additive binary response models...

The paper is concerned with the problem of variance estimation for a high-dimensional regression model. The results show that the accuracy n -1/2 of variance estimation can be achieved only under some restrictions on smoothness properties of the regression function and on the dimensionality of...