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...

Additive modelling has been widely used in nonparametric regression to circumvent the "curse of dimensionality", by reducing the problem of estimating a multivariate regression function to the estimation of its univariate components. Estimation of these univariate functions, however, can suffer...

Additive modelling is known to be useful for multivariate nonparametric regression as it reduces the complexity of problem to the level of univariate regression. This usefulness could be compromised if the data set was contaminated by outliers whose detection and removal are particularly...

A general model specification test of a parametric model against a nonparametric or semiparametric alternative is studied. The test statistic employs a fixed kernel, not varying by a bandwidth. This test is proved to be consistent, the asymptotic distribution is derived and shown to be...

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...

Consider the regression y = f(x) + e ' where E (e | x) = 0 and the exact functional form of f is unknown, although we do know that it is homogeneous of known degree r. Using a local linear approach we examine two ways of nonparametrically estimating f: (i) a "direct" or "numeraire" approach, and...