Modelization and Nonparametric estimation for a dynamical system with noise

International audienceWe examine the effect of two specific noises on a dynamical system. We obtain consistent estimates with their rates of convergence for the invariant density for such a model. Some simulations are provided

Estimation du paramètre des moyennes mobiles hilbertiennes

The moving average processes in a separable infinite-dimensional Hilbert space H, denoted by MAH ( 1 ) , is a H valued process ( X t , t ∈ Z ) satisfying the equation X t = ϵ t + l ( ϵ t − 1 ) where l is a compact operator in H and ( ϵ t ) a H valued strong white noise. In this Note we propose two estimators for l based on the moment equation of the process

Dielectric selective mirror for intracavity wavelength selection in far-infrared p-Ge lasers

A robust metal-free intracavity fixed-wavelength selector for the cryogenically cooled far-infrared p-Ge laser is demonstrated. The device is a back mirror consisting of a thin silicon etalon and dielectric SrTiO3 flat. A laser line width of 0.2 cm-1 is achieved, which corresponds to an active cavity finesse of similar to0.15. The wavelength position and spectral purity are maintained over a wide range of laser operating fields. Use of SrTiO3 lowers the laser resonance line frequencies by similar to1 cm-1 compared with expectations for metal mirrors. The effect is due to phase shift, which is determined from far-infrared reflectivity measurements of SrTiO3. A p-Ge laser with such selector is free from danger of electrical breakdown and mirror oxidation during repeatable thermal cycling, which makes it more reliable than previous selection schemes for practical applications

Asymptotic normality of the Parzen-Rosenblatt density estimator for strongly mixing random fields

We prove the asymptotic normality of the kernel density estimator (introduced by Rosenblatt (1956) and Parzen (1962)) in the context of stationary strongly mixing random fields. Our approach is based on the Lindeberg's method rather than on Bernstein's small-block-large-block technique and coupling arguments widely used in previous works on nonparametric estimation for spatial processes. Our method allows us to consider only minimal conditions on the bandwidth parameter and provides a simple criterion on the (non-uniform) strong mixing coefficients which do not depend on the bandwith.Comment: 16 page

Inverse Problems in a Bayesian Setting

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.Comment: arXiv admin note: substantial text overlap with arXiv:1312.504

CLT in Functional Linear Regression Models

International audienceWe propose in this work to derive a CLT in the functional linear regression model to get confidence sets for prediction based on functional linear regression. The main difficulty is due to the fact that estimation of the functional parameter leads to a kind of ill-posed inverse problem. We consider estimators that belong to a large class of regularizing methods and we first show that, contrary to the multivariate case, it is not possible to state a CLT in the topology of the considered functional space. However, we show that we can get a CLT for the weak topology under mild hypotheses and in particular without assuming any strong assumptions on the decay of the eigenvalues of the covariance operator. Rates of convergence depend on the smoothness of the functional coefficient and on the point in which the prediction is made

High Resolution Genome-Wide Analysis of Chromosomal Alterations in Burkitt's Lymphoma

Additional chromosomal abnormalities are currently detected in Burkitt's lymphoma. They play major roles in the progression of BL and in prognosis. The genes involved remain elusive. A whole-genome oligonucleotide array CGH analysis correlated with karyotype and FISH was performed in a set of 27 Burkitt's lymphoma-derived cell lines and primary tumors. More than half of the 145 CNAs<2 Mb were mapped to Mendelian CNVs, including GSTT1, glutathione s-transferase and BIRC6, an anti-apoptotic protein, possibly predisposing to some cancers. Somatic cell line-specific CNVs localized to the IG locus were consistently observed with the 244 K aCGH platform. Among 136 CNAs >2 Mb, gains were found in 1q (12/27), 13q (7/27), 7q (6/27), 8q(4/27), 2p (3/27), 11q (2/27) and 15q (2/27). Losses were found in 3p (5/27), 4p (4/27), 4q (4/27), 9p (4/27), 13q (4/27), 6p (3/27), 17p (3/27), 6q (2/27),11pterp13 (2/27) and 14q12q21.3 (2/27). Twenty one minimal critical regions (MCR), (range 0.04–71.36 Mb), were delineated in tumors and cell lines. Three MCRs were localized to 1q. The proximal one was mapped to 1q21.1q25.2 with a 6.3 Mb amplicon (1q21.1q21.3) harboring BCA2 and PIAS3. In the other 2 MCRs, 1q32.1 and 1q44, MDM4 and AKT3 appeared as possible drivers of these gains respectively. The 13q31.3q32.1 <89.58–96.81> MCR contained an amplicon and ABCC4 might be the driver of this amplicon. The 40 Kb 2p16.1 <60.96–61> MCR was the smallest gained MCR and specifically encompassed the REL oncogene which is already implicated in B cell lymphomas. The most frequently deleted MCR was 3p14.1 <60.43–60.53> that removed the fifth exon of FHIT. Further investigations which combined gene expression and functional studies are essential to understand the lymphomagenesis mechanism and for the development of more effective, targeted therapeutic strategies