Ignoring the model selection step in inference after selection is harmful. This paper studies the asymptotic distribution of estimators after model selection using the Akaike information criterion. First, we consider the classical setting in which a true model exists and is included in the...

Variable selection in the presence of outliers may be performed by using a robust version of Akaike's information criterion AIC. In this paper explicit expressions are obtained for such criteria when S and MM-estimators are used. The performance of these criteria is compared to the existing AIC...

Phase variation in functional data obscures the true amplitude variation when a typical cross-sectional analysis of these responses would be performed. Time warping or curve registration aims at eliminating the phase variation, typically by applying a transformation, the warping function 'pi' ,...

A new method for model selection for Gaussian directed acyclic graphs (DAG) and Gaussian graphical models (GGM), with extensions towards ancestral graphs (AG), is constructed to have good prediction properties. The method is based on the focused information criterion, and offers the possibility...

Mixed models, with both random and fixed effects, are most often estimated on the assumption that the random effects are normally distributed. In this paper we propose several formal tests of the hypothesis that the random effects and/or errors are normally distributed. Most of the proposed...

In this paper, we di fferentiate between isotropic and hyperbolic wavelet bases in the context of multivariate nonparametric function estimation. The study of the latter leads to new phenomena and non trivial extensions of univariate studies. In this context, we fi rst exhibit the limitations of...

We consider the problem of model selection for quantile regression analysis where a particular purpose of the modeling procedure has to be taken into account. Typical examples include estimation of the area under the curve in pharmacokinetics or estimation of the minimum eff ective dose in phase...

A multivariate depth for functional data is defined and studied. By the multivariate nature and by including a weight function, it acknowledges important characteristics of functional data, namely differences in the amount of local amplitude, shape and phase variation. Both population and finite...

We develop nonparametric tests for the null hypothesis that a function has a prescribed form, to apply to data sets with missing observations. Omnibus nonparametric tests do not need to specify a particular alternative parametric form, and have power against a large range of alternatives, the...