Dominique Bontemps
About adaptive coding on countable alphabets.
Thu, 02/02/2012 - 15:01 — SomNambulAuthors: Dominique Bontemps, Elisabeth Gassiat, Stéphane Boucheron
Subjects: Statistics
AbstractThis paper sheds light on universal coding with respect to classes of
memoryless sources over a countable alphabet defined by an envelope function
with finite and non-decreasing hazard rate. We prove that the auto-censuring AC
code introduced by Bontemps (2011) is adaptive with respect to the collection
of such classes. The analysis builds on the tight characterization of universal
redundancy rate in terms of metric entropy % of small source classes by Opper
and Haussler (1997) and on a careful analysis of the performance of the
AC-coding algorithm.Bernstein von Mises Theorems for Gaussian Regression with increasing number of regressors.
Wed, 09/08/2010 - 15:01 — SomNambulAuthors: Dominique Bontemps
Subjects: Statistics
AbstractThis paper brings a contribution to the Bayesian theory of nonparametric and
semiparametric estimation. We are interested in the asymptotic normality of the
posterior distribution in Gaussian linear regression models when the number of
regressors increases with the sample size.A new penalized criterion for variable selection and clustering using genotypic data.
Mon, 02/08/2010 - 16:01 — SomNambulAuthors: Dominique Bontemps, Wilson Toussile
Subjects: Statistics
AbstractWe consider the problem of estimating the number of components and the
relevant variables in a mixture model for multilocus genotypic data. A new
penalized maximum likelihood criterion is proposed, and a non-asymptotic oracle
inequality is obtained. Further, under weak assumptions on the true probability
underlying the observations, the selected model is asymptotically consistent.
On a practical aspect, the shape of our proposed penalty function is defined up
to a multiplicative constant which is calibrated thanks to the slope
heuristics, in an automatic data-driven procedure.
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