## The probability versions for the Big-O and little-o notations

We introduce here some notation very useful in probability and statistics. Definition 1 For a given sequence of random variables \$latex {R_{n}}&fg=000000\$, \$latex {(i)}&fg=000000\$ \$latex {X_{n}=o_{P}(R_{n})}&fg=000000\$ means \$latex {X_{n}=Y_{n}R_{n}}&fg=000000\$ with \$latex {Y_{n}}&fg=000000\$ converging to \$latex 0&fg=000000\$ in probability. \$latex {(ii)}&fg=000000\$ \$latex {X_{n}=O_{P}(R_{n})}&fg=000000\$ means \$latex {X_{n}=Y_{n}R_{n}}&fg=000000\$ with the family \$latex {(Y_{n})_{n}}&fg=000000\$ uniformly thigh.

## “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 […]

## The Slutsky’s lemma as an application of the continuous mapping theorem and uniform weak convergence

Photo of Evgeny Evgenievich Slutsky. Sources: MacTutor and Bomkj. Applying the continuous mapping theorem and \$latex {(v)}&fg=000000\$ from the last post, we get the following theorem Lemma (Slutsky). Let be \$latex {X_{n}}&fg=000000\$, \$latex {X}&fg=000000\$ and \$latex {Y_{n}}&fg=000000\$ random vectors and \$latex {c}&fg=000000\$ a constant vector. If \$latex {X_{n}\rightsquigarrow X}&fg=000000\$ and \$latex {Y_{n}\rightsquigarrow c}&fg=000000\$, then \$latex […]

## Some relationships between different modes of convergence

We are going to show some relations between the different modes of convergence . These results are very important in practical examples. In the next post we will explain some of them. To proof this theorem, we shall use several times the Portmanteau’s lemma.