## “Sometimes You Just Have to Jump out the Window and Grow Wings on the Way Down”

http://youtu.be/sLuDOEuwwso

“Sometimes You Just Have to Jump out the Window and Grow Wings on the Way Down”

## Semaine d’Etude “Mathématiques et Entreprise”

Working on the “Elaboration of physics models for road traffic” (http://www.math.univ-toulouse.fr/SEME/) Abstract (in French) La modélisation du trafic routier est un sujet abordé dans de nombreux domaines. L’objectif est de mettre en parallèle deux d’entre eux: la physique et la statistique. La modélisation physique du trafic routier repose sur la loi de conservation des véhicules …

## AuthorAID

Few days ago I signed-up into AuthorAID. This program helps to researchers from developing countries to get experience preparing scientific articles for publication in peer-reviewed journals. You can check my profile at http://www.authoraid.info/author/maikolsolis Moreover, the news section gives useful tips and resources about things related to this preparation.  http://www.authoraid.info/news Let me know in the comments if you …

## JdS 2012: Efficient estimation of conditional covariance matrices for dimension reduction

In the framework of the Journées de Statisque 2012 in Bruxelles, I presented the paper “Efficient estimation of conditional covariance matrices” made under Jean-Michel Loubes and Clement Marteau direction. You could check the program and the slides of the presentation. Today I will present you some ideas about the problem studied and the solution found …

## Distribution function, weak convergence and Portmanteau’s lemma.

1. Preliminaries Given a random variable $latex {X}&fg=000000$, we define the cumulative distribution function(or distribution function) as follows,

## Multivariate kernel density estimation

Briefly, we shall see the definition of a kernel density estimator in the multivariate case. Suppose that the data is d-dimensional so that $latex {X_{i}=(X_{i1},\ldots,X_{id})}&fg=000000$. We will use the product kernel $latex \displaystyle \hat{f}_{h}(x)=\frac{1}{nh_{1}\cdots h_{d}}\left\{ \prod_{j=1}^{d}K\left(\frac{x_{j}-X_{ij}}{h_{j}}\right)\right\} . &fg=000000$ The risk is given by $latex \displaystyle \mathrm{MISE}\approx\frac{\left(\mu_{2}(K)\right)^{4}}{4}\left[\sum_{j=1}^{d}h_{j}^{4}\int f_{jj}^{2}(x)dx+\sum_{j\neq k}h_{j}^{2}h_{k}^{2}\int f_{jj}f_{kk}dx\right]+\frac{\left(\int K^{2}(x)dx\right)^{d}}{nh_{1}\cdots h_{d}} &fg=000000$