Global smoothness estimation of a Gaussian process from regular sequence designs

We consider a real Gaussian process $X$ having a global unknown smoothness $(r_{\scriptscriptstyle 0},\beta_{\scriptscriptstyle 0})$, r_{\scriptscriptstyle 0}\in \mathds{N}_0 and $\beta_{\scriptscriptstyle 0} \in]0,1[$, with $X^{(r_{\scriptscriptstyle 0})}$ (the mean-square derivative of $X$ if $r_{\scriptscriptstyle 0}\ge 1$) supposed to be locally stationary with index $\beta_{\scriptscriptstyle 0}$. From the behavior of quadratic variations built on divided differences of $X$, we derive an estimator of $(r_{\scriptscriptstyle 0},\beta_{\scriptscriptstyle 0})$ based on - not necessarily equally spaced - observations of $X$. Various numerical studies of these estimators exhibit their properties for finite sample size and different types of processes, and are also completed by two examples of application to real data.Comment: 28 page

Assessing the number of mean-square derivatives of a Gaussian process

28 pagesInternational audienceWe consider a real Gaussian process $X$ with unknown smoothness \ro\in\n_{ßte 0} where the mean-square derivative X^{(\ro)} is supposed to be H\"{o}lder continuous in quadratic mean. First, from the discrete observations $X(t_1), \dotsc, X(t_n)$, we study reconstruction of $X(t)$, $t\in[0,1]$ with $\widetilde{X}_r(t)$, a piecewise polynomial interpolation of degree $r\ge 1$. We show that the mean-square error of interpolation is a decreasing function of $r$ but becomes stable as soon as r\ge \ro. Next, from an interpolation-based empirical criterion, we derive an estimator $\widehat{r}$ of \ro and prove its strong consistency by giving an exponential inequality for P(\widehat{r}\not=\ro). Finally, we prove the strong consistency of $\widetilde{X}_{\widehat{r}}(t)$ with an almost optimal rate

Artificial boundary conditions to compute correctors in linear elasticity

International audienceIn this paper, we derive artificial boundary conditions for the computation of correcting terms in a perturbed problem of linear elasticity. Theses conditions appear to be of Ventcel form, and lead to a non-coercive boundary value problem

Global smoothness estimation of a Gaussian process from general sequence designs.

International audienceWe consider a real Gaussian process X with global unknown smoothness (r0, β0): more precisely X (r 0) , r0 ∈ N 0 , is supposed to be locally stationary with Hölder exponent β0, β0 ∈]0, 1[. For X observed at a finite set of points, we derive estimators of r0 and β0 based on the quadratic variations for the divided differences of X. Under mild conditions, we obtain an exponential bound for estimating r0, as well as sharp rates of convergence (up to logarithmic factors) for the estimation of β0. An extensive simulation study illustrates the finite-sample properties of both estimators for different types of processes and we also include two real data applications

Estimating the order of mean-square derivatives with quadratic variations

International audienc

EVALUATION DE LA CHARGE PARASITAIRE DANS LE LIQUIDE AMNIOTIQUE AU COURS DE LA TOXOPLASMOSE CONGENITALE PAR PCR QUANTITATIVE (DES BIOL. MED.)

LYON1-BU Santé (693882101) / SudocSudocFranceF

Assessing the number of mean square derivatives of a Gaussian process

We consider a real Gaussian process X with unknown smoothness where the mean square derivative X(r0) is supposed to be Hölder continuous in quadratic mean. First, from selected sampled observations, we study the reconstruction of X(t), t[set membership, variant][0,1], with a piecewise polynomial interpolation of degree r>=1. We show that the mean square error of the interpolation is a decreasing function of r but becomes stable as soon as r>=r0. Next, from an interpolation-based empirical criterion and n sampled observations of X, we derive an estimator of r0 and prove its strong consistency by giving an exponential inequality for . Finally, we establish the strong consistency of with an almost optimal rate.Inference for Gaussian processes Holder regularity Piecewise Lagrange interpolation Regular sequences

An new methodology to optimize the efficiency of a multi-sources and multi-converters system under harmonic constraints. Application to light rail systems

International audienceA new HVDC power supply network for light rail systems is presented and compared to classical distribution networks based on AC/DC controlled converters. This original supply network use an intermediate high voltage DC feeder which supplies the vehicle through simple synchronous buck converters. Nevertheless, as the number of substations can be increased to improve the line voltage control, harmonic interactions between substations may increase both. Therefore, an adapted tool of power converter filter design has to be developed for such a dynamic complex system with power electronics converters, AC and DC networks, moving vehicles and harmonic interactions. After a brief presentation of the supply network, two levels of modelling are then presented. A dynamic model is first described by using a generalized state-space averaging model of converters, which takes into account global losses in converters for switching and conduction phases. Then, ta second model is proposed to optimize the parameters of input and output filters of converters according to maximal current and voltage ripples. Finally, this methodology of sizing is applied on a simplified supply network of light rail

Simulating calculations and optimization design of a new HVDC supply power for light rail system

International audienceIn this paper, a new HVDC power supply system for light rail systems is presented and compared to classical distribution networks based on AC/DC controlled converters. A simulation tool has been developed to simulate such a complex system, taking into account vehicle motion and HVDC electrical distribution. Then, an optimization of HVDC structure and control will be presented using Lagrangian formulation. All the results are compared to classical distributions, and show the effectiveness of the proposed power supply distribution used for light rail systems