26 research outputs found
Non-uniform spline recovery from small degree polynomial approximation
We investigate the sparse spikes deconvolution problem onto spaces of
algebraic polynomials. Our framework encompasses the measure reconstruction
problem from a combination of noiseless and noisy moment measurements. We study
a TV-norm regularization procedure to localize the support and estimate the
weights of a target discrete measure in this frame. Furthermore, we derive
quantitative bounds on the support recovery and the amplitudes errors under a
Chebyshev-type minimal separation condition on its support. Incidentally, we
study the localization of the knots of non-uniform splines when a Gaussian
perturbation of their inner-products with a known polynomial basis is observed
(i.e. a small degree polynomial approximation is known) and the boundary
conditions are known. We prove that the knots can be recovered in a grid-free
manner using semidefinite programming
Generalization of the Nualart-Peccati criterion
The celebrated Nualart-Peccati criterion [Ann. Probab. 33 (2005) 177-193]
ensures the convergence in distribution toward a standard Gaussian random
variable of a given sequence of multiple Wiener-It\^{o}
integrals of fixed order, if and . Since its appearance in 2005, the natural
question of ascertaining which other moments can replace the fourth moment in
the above criterion has remained entirely open. Based on the technique recently
introduced in [J. Funct. Anal. 266 (2014) 2341-2359], we settle this problem
and establish that the convergence of any even moment, greater than four, to
the corresponding moment of the standard Gaussian distribution, guarantees the
central convergence. As a by-product, we provide many new moment inequalities
for multiple Wiener-It\^{o} integrals. For instance, if is a normalized
multiple Wiener-It\^{o} integral of order greater than one, Comment: Published at http://dx.doi.org/10.1214/14-AOP992 in the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
An algebra of Stein operators
We build upon recent advances on the distributional aspect of Stein's method
to propose a novel and flexible technique for computing Stein operators for
random variables that can be written as products of independent random
variables. We show that our results are valid for a wide class of distributions
including normal, beta, variance-gamma, generalized gamma and many more. Our
operators are th degree differential operators with polynomial coefficients;
they are straightforward to obtain even when the target density bears no
explicit handle. As an application, we derive a new formula for the density of
the product of independent symmetric variance-gamma distributed random
variables.Comment: 20 page
On the rate of convergence in de Finetti's representation theorem
A consequence of de Finetti's representation theorem is that for every
infinite sequence of exchangeable 0-1 random variables , there
exists a probability measure on the Borel sets of such that converges weakly to . For a wide class of
probability measures having smooth density on , we give bounds of
order with explicit constants for the Wasserstein distance between the
law of and . This extends a recent result {by} Goldstein and
Reinert \cite{goldstein2013stein} regarding the distance between the scaled
number of white balls drawn in a P\'olya-Eggenberger urn and its limiting
distribution. We prove also that, in the most general cases, the distance
between the law of and is bounded below by and above by
(up to some multiplicative constants). For every , we give an example of an exchangeable sequence such that this
distance is of order
Modélisation du processus d'inclusion de patients dans un essai clinique multicentrique
Cette thèse a pour objet la modélisation statistique du processus d'inclusion de patients lors de la phase III d'un essai clinique multicentrique. Elle présente les modèles bayésiens empiriques existants (modèle Gamma-Poisson) et en propose de nouveaux, prenant en compte une incertitude sur la date d'ouverture des centres ou une intensité d'inclusion dépendant du temps. Sont abordés les problèmes d'estimation et prédiction du nombre de patients inclus à partir d'une étude à une date intermédiaire. Un modèle bayésien prenant en compte la perte de patients en phase de screening est également introduit. Enfin, un modèle de coût s'appuyant sur les modèles précédents est proposé.In this work, we investigate the statistical modeling of the patients' inclusion process in phase III of a multicentric clinical trial. We introduce empirical bayesian models similar to the Gamma-Poisson process that take into account uncertainty in the opening dates of centers or a time-dependent rate of inclusion. We show how to perform estimation and prediction based on an on-going study at some interim time. We extend these models to account for patients drop-out during screening process. Finally, a stochastic cost model is proposed
Stein operators, kernels and discrepancies for multivariate continuous distributions
We present a general framework for setting up Stein's method for multivariate continuous distributions. The approach gives a collection of Stein characterizations, among which we highlight score-Stein operators and kernel-Stein operators. Applications include copu-las and distance between posterior distributions. We give a general explicit construction for Stein kernels for elliptical distributions and discuss Stein kernels in generality, highlighting connections with Fisher information and mass transport. Finally, a goodness-of-fit test based on Stein discrepancies is given
Some new Stein operators for product distributions
We provide a general result for finding Stein operators for the product of
two independent random variables whose Stein operators satisfy a certain
assumption, extending a recent result of Gaunt, Mijoule and Swan \cite{gms18}.
This framework applies to non-centered normal and non-centered gamma random
variables, as well as a general sub-family of the variance-gamma distributions.
Curiously, there is an increase in complexity in the Stein operators for
products of independent normals as one moves, for example, from centered to
non-centered normals. As applications, we give a simple derivation of the
characteristic function of the product of independent normals, and provide
insight into why the probability density function of this distribution is much
more complicated in the non-centered case than the centered case.Comment: 18 pages. To appear in Brazilian Journal of Probability and
Statistics, 2019
Stein operators, kernels and discrepancies for multivariate continuous distributions
We present a general framework for setting up Stein's method for multivariate continuous distributions. The approach gives a collection of Stein characterizations, among which we highlight score-Stein operators and kernel-Stein operators. Applications include copu-las and distance between posterior distributions. We give a general explicit construction for Stein kernels for elliptical distributions and discuss Stein kernels in generality, highlighting connections with Fisher information and mass transport. Finally, a goodness-of-fit test based on Stein discrepancies is given
TARJETA POSTAL ROMÁNTICA [Material gráfico]
FRANCIACopia digital. Madrid : Ministerio de Educación, Cultura y Deporte, 201