## vector quantile regression

Posted in pictures, Statistics, University life with tags , , , , , , , on July 4, 2014 by xi'an

My Paris-Dauphine colleague Guillaume Carlier recently arXived a statistics paper entitled Vector quantile regression, co-written with Chernozhukov and Galichon. I was most curious to read the paper as Guillaume is primarily a mathematical analyst working on optimisation problems like optimal transport. And also because I find quantile regression difficult to fathom as a statistical problem. (As it happens, both his co-authors are from econometrics.) The results in the paper are (i) to show that a d-dimensional (Lebesgue) absolutely continuous random variable Y can always be represented as the deterministic transform Y=Q(U), where U is a d-dimensional [0,1] uniform (the paper expresses this transform as conditional on a set of regressors Z, but those essentially play no role) and Q is monotonous in the sense of being the gradient of a convex function,

$Q(u) = \nabla q(u)$ and $\{Q(u)-Q(v)\}^\text{T}(u-v)\ge 0;$

(ii) to deduce from this representation a unique notion of multivariate quantile function; and (iii) to consider the special case when the quantile function Q can be written as the linear

$\beta(U)^\text{T}Z$

where β(U) is a matrix. Hence leading to an estimation problem.

While unsurprising from a measure theoretic viewpoint, the representation theorem (i) is most interesting both for statistical and simulation reasons. Provided the function Q can be easily estimated and derived, respectively. The paper however does not provide a constructive tool for this derivation, besides indicating several characterisations as solutions of optimisation problems. From a statistical perspective, a non-parametric estimation of  β(.) would have useful implications in multivariate regression, although the paper only considers the specific linear case above. Which solution is obtained by a discretisation of all variables and  linear programming.

## Statistical modeling and computation [apologies]

Posted in Books, R, Statistics, University life with tags , , , , , , , , , , , on June 11, 2014 by xi'an

In my book review of the recent book by Dirk Kroese and Joshua Chan,  Statistical Modeling and Computation, I mistakenly and persistently typed the name of the second author as Joshua Chen. This typo alas made it to the printed and on-line versions of the subsequent CHANCE 27(2) column. I am thus very much sorry for this mistake of mine and most sincerely apologise to the authors. Indeed, it always annoys me to have my name mistyped (usually as Roberts!) in references.  [If nothing else, this typo signals it is high time for a change of my prescription glasses.]

## Statistical modeling and computation [book review]

Posted in Books, R, Statistics, University life with tags , , , , , , , , , , , , , on January 22, 2014 by xi'an

Dirk Kroese (from UQ, Brisbane) and Joshua Chan (from ANU, Canberra) just published a book entitled Statistical Modeling and Computation, distributed by Springer-Verlag (I cannot tell which series it is part of from the cover or frontpages…) The book is intended mostly for an undergrad audience (or for graduate students with no probability or statistics background). Given that prerequisite, Statistical Modeling and Computation is fairly standard in that it recalls probability basics, the principles of statistical inference, and classical parametric models. In a third part, the authors cover “advanced models” like generalised linear models, time series and state-space models. The specificity of the book lies in the inclusion of simulation methods, in particular MCMC methods, and illustrations by Matlab code boxes. (Codes that are available on the companion website, along with R translations.) It thus has a lot in common with our Bayesian Essentials with R, meaning that I am not the most appropriate or least unbiased reviewer for this book. Continue reading

## MCQMC2014 in Belgium

Posted in Books, Statistics, Travel, University life with tags , , , , , , , , , on October 11, 2013 by xi'an

The conference MCQMC2014 (which stands for Monte Carlo and Quasi-Monte Carlo) will take place in Leuven, Belgium, on April 6-11. More exactly, in the Katholieke Universiteit Leuven, which is the Flemish-speaking side of the split (1968) Catholic University of Leuven, the French speaking side Université Catholique de Louvain being located in Louvain-la-Neuve. After missing MCQMC2012 in Sydney,  I will attend this conference where I give an invited talk (on ABC, what else..?!). As it happens (and kind of logically), I have visited Louvain-la-Neuve many times, especially in the previous era where historical Bayesians Michel Mouchard, Jean-Marie Rolin and Léopold Simar were together in the Statistics department—two of them contributing to the highly formalised “Elements of Bayesian Statistics” that I perused during my PhD thesis in Rouen—, but I have never been to Leuven or to KU Leuven,

A great item of news is that one of the two tutorials (on April 6, 2014) will given by Art Owen, the theme being “ANOVA, global sensitivity, Sobol’ indices and all that“, The second tutorial is by Mike Giles (Oxford) on his approach of multi-level Monte Carlo methods. (If the organisers follow the MCQMC2012 trend, the Sunday afternoon tutorials should follow one another.)

## 9th IMACS seminar on Monte Carlo Methods, Annecy

Posted in Mountains, pictures, R, Running, Statistics, Travel, University life with tags , , , , , , , , , , on July 18, 2013 by xi'an

As astute ‘Og’s readers may have gathered (!), I am now in Annecy, Savoie, for the 9th IMACS seminar on Monte Carlo Methods. Where I was kindly invited to give a talk on ABC. IMACS stands for “International Association for Mathematics and Computers in Simulation” and the conference gathers themes and sensibilities I am not familiar with. And very few statisticians. For instance, I attended a stochastic particle session that had nothing to do with my understanding of particle systems (except for Pierre Del Moral’s mean field talk). The overall focus seems to stand much more around SDEs and quasi-Monte Carlo methods. Both items for which I have a genuine interest but little background, so I cannot report much on the talks I have attended beyond reporting their title. I for instance discovered the multilevel Monte Carlo techniques for SDEs, which sounds like a control variate methodology to reduce the variance w/o reducing the discretisation step. (Another instance is that the proceedings will be published in Mathematics and Computers in Simulation or Monte Carlo Methods and Applications. Two journals I have never published in.) Although I have yet a few months before attending my first MCQMC conference, I presume this is somehow a similar spirit and mix of communities.

At another level, attending a conference in Annecy is a blessing: the city is beautiful, the lake pristine and tantalising in the hot weather, and the surrounding mountains (we are actually quite close to Chamonix!) induce me to go running on both mornings and evenings.