In this paper we consider kernel estimation of a density when the data are contaminated by random noise. More specifically we deal with the problem of how to choose the bandwidth parameter in practice.

We propose a kernel estimator of integrated squared density derivatives, from a sample that has been contaminated by random noise. We derive asymptotic expressions for the bias and the variance of the estimator and show that the squared bias term dominates the variance term. This coincides with...

The infinite dimension of functional data can challenge conventional methods for classification and clustering. A variety of techniques have been introduced to address this problem, particularly in the case of prediction, but the structural models that they involve can be too inaccurate, or too...

In this paper the interest is in testing whether a regression function is polynomial of a certain degree. One possible approach to this testing problem is to do a parametric polynomial fit and a nonparametric fit and to reject the null hypothesis of a polynomial function if the distance between...

Generalized Linear Models are a widely used method to obtain parametric es- timates for the mean function. They have been further extended to allow the re- lationship between the mean function and the covariates to be more flexible via Generalized Additive Models. However the fixed variance...

This paper proposes a robust forecasting method for non-stationary time series. The time series is modelled using non-parametric heteroscedastic regression, and fitted by a localized MM-estimator, combining high robustness and large efficiency. The proposed method is shown to produce reliable...

Robust selection of variables in a linear regression model is investigated. Many variable selection methods are available, but very few methods are designed to avoid sensitivity to vertical outliers as well as to leverage points. The nonnegative garrote method is a powerful variable selection...