Functional limit laws for the increments of the quantile process; with applications

We establish a functional limit law of the logarithm for the increments of the normed quantile process based upon a random sample of size $n\to\infty$. We extend a limit law obtained by Deheuvels and Mason (12), showing that their results hold uniformly over the bandwidth $h$, restricted to vary in $[h'_n,h''_n]$, where $\{h'_n\}_{n\geq1}$ and $\{h''_n\}_{n\geq 1}$ are appropriate non-random sequences. We treat the case where the sample observations follow possibly non-uniform distributions. As a consequence of our theorems, we provide uniform limit laws for nearest-neighbor density estimators, in the spirit of those given by Deheuvels and Mason (13) for kernel-type estimators.Comment: Published in at http://dx.doi.org/10.1214/07-EJS099 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Regression modeling on stratified data with the lasso

We consider the estimation of regression models on strata defined using a categorical covariate, in order to identify interactions between this categorical covariate and the other predictors. A basic approach requires the choice of a reference stratum. We show that the performance of a penalized version of this approach depends on this arbitrary choice. We propose a refined approach that bypasses this arbitrary choice, at almost no additional computational cost. Regarding model selection consistency, our proposal mimics the strategy based on an optimal and covariate-specific choice for the reference stratum. Results from an empirical study confirm that our proposal generally outperforms the basic approach in the identification and description of the interactions. An illustration on gene expression data is provided.Comment: 23 pages, 5 figure

On some limitations of probabilistic models for dimension-reduction: illustration in the case of one particular probabilistic formulation of PLS

Partial Least Squares (PLS) refer to a class of dimension-reduction techniques aiming at the identification of two sets of components with maximal covariance, in order to model the relationship between two sets of observed variables $x\in\mathbb{R}^p$ and $y\in\mathbb{R}^q$, with $p\geq 1, q\geq 1$. El Bouhaddani et al. (2017) have recently proposed a probabilistic formulation of PLS. Under the constraints they consider for the parameters of their model, this latter can be seen as a probabilistic formulation of one version of PLS, namely the PLS-SVD. However, we establish that these constraints are too restrictive as they define a very particular subset of distributions for $(x,y)$ under which, roughly speaking, components with maximal covariance (solutions of PLS-SVD), are also necessarily of respective maximal variances (solutions of the principal components analyses of $x$ and $y$, respectively). Then, we propose a simple extension of el Bouhaddani et al.'s model, which corresponds to a more general probabilistic formulation of PLS-SVD, and which is no longer restricted to these particular distributions. We present numerical examples to illustrate the limitations of the original model of el Bouhaddani et al. (2017)

Guerre e paci veneto-turche dal 1453 al 1573

Atti del XV convegno internazionale di Chianciano-PienzaCe travail entend souligner comment les conflits entre Venise et les Turcs Ottomans constituent les épisodes d'une unique guerre, comme la guerre de Cent ans qui a opposé la France et l'Angleterre de 1337 à 1433.Vorremmo tentare di evidenziare come le diverse fasi di pace e di guerra che alternano nelle relazioni veneto-turche dal 1453 al 1573 siano, in fatti, un'unica guerra, tipo guerra dei Cent'Anni che contrappose Francia e Inghilterra dal 1337 al 1433. Limiteremo il nostro discorso al 1573 —anche se l'ipotesi ci sembra valida fino al 1669— prima per entrare nei limiti intellettuali del convegno e poi perchè la battaglia di Lepanto fu una vittoria non sfruttata che però rappresentò la fine del mito terrificante dell'invincibilità turca, come l'abbiamo già sottolineato

Véronèse : noces et banquets

The Veronese's painting "Nozze di Cana" is not explained with history of art rules but as a religious painting and an evidence of venitian way of life in the 16th century.Une double lecture des "Noces de Cana" de Véronèse en examinant d'abord la fidélité du peintre au texte de l'Evangile de Jean (2,1-11) puis en prenant en considération la parfaite mise en scène et illustration des traités de l'art de la table en cours dans la Venise du XVIe siècle