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.

Semaine d’Etude “Mathématiques et Entreprise”

Working on the “Elaboration of physics models for road traffic” ( 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 […]


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 Moreover, the news section gives useful tips and resources about things related to this preparation. 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 […]