Remark on the finite-dimensional character of certain results of functional statistics

4 pagesInternational audienceThis note shows that some assumption on small balls probability, frequently used in the domain of functional statistics, implies that the considered functional space is of finite dimension. To complete this result an example of L2 process is given that does not fulfill this assumption

A moment approach for the almost sure central limit theorem for martingales

19 pagesInternational audienceWe prove the almost sure central limit theorem for martingales via an original approach which uses the Carleman moment theorem together with the convergence of moments for powers of martingales. Several statistical applications on autoregressive and branching processes are also provided

New Fréchet features for random distributions and associated sensitivity indices

In this article we define new Fréchet features for random cumulative distribution functions using contrast. These contrasts allow to construct Wasserstein costs and our new features minimize the average costs as the Fréchet mean minimizes the mean square Wasserstein2 distance. An example of new features is the median, and more generally the quantiles. From these definitions, we are able to define sensitivity indices when the random distribution is the output of a stochastic code. Associated to the Fréchet mean we extend the Sobol indices, and in general the indices associated to a contrast that we previously proposed

New sensitivity analysis subordinated to a contrast

International audienceIn a model of the form $Y=h(X_1,\ldots,X_d)$ where the goal is to estimate a parameter of the probability distribution of $Y$, we define new sensitivity indices which quantify the importance of each variable $X_i$ with respect to this parameter of interest. The aim of this paper is to define {\it goal oriented sensitivity indices} and we will show that Sobol indices are sensitivity indices associated to a particular characteristic of the distribution $Y$. We name the framework we present as {\it Goal Oriented Sensitivity Analysis} (GOSA)

Risk bounds for new M-estimation problems

International audienceIn this paper, we develop new algorithms for parameter estimation in the case of models type Input/Output in order to represent and to characterize a phenomenon Y. From experimental data Y_{1},...,Y_{n} supposed to be i.i.d from Y, we prove risk bounds qualifying the proposed procedures in terms of the number of experimental data n, computing budget m and model complexity. The methods we present are general enough which should cover a wide range of applications

Stochastic inverse problem with noisy simulator - Application to aeronautical model

International audienceInverse problem is a current practice in engineering where the goal is to identify parameters from observed data through numerical models. These numerical models, also called Simulators, are built to represent the phenomenon making possible the inference. However, such representation can include some part of variability or commonly called uncertainty (see [4]), arising from some variables of the model. The phenomenon we study is the fuel mass needed to link two given countries with a commercial aircraft, where we only consider the Cruise phase . From a data base of fuel mass consumptions during the cruise phase, we aim at identifying the Speci c Fuel Consumption (SFC) in a robust way, given the uncertainty of the cruise speed V and the lift-to-drag ratio F. In this paper, we present an estimation procedure based on Maximum-Likelihood estimation, taking into account this uncertainty

Integrity Based on MT28 for EGNOS: New Algorithm Formulation & Results

The purpose of a Satellite Based Augmentation System, such as EGNOS or WAAS, is to decompose all range error sources and to distribute them to the civil aviation user community with reliable navigation services for different flight phases. Integrity refers to the notion of trust that the user may have in the positioning. Integrity includes the ability of the system to provide confidence thresholds as well as Alarms in case of anomalies. Considering satellite integrity, two ways are possible for an SBAS. The first is to broadcast per satellite the same UDRE value applicable for every user located inside the service area defined by the message type 27 content. As these UDREs are dimensioned to protect the worst user location – generally at the border zone – it penalizes automatically the users having lower residual errors. The second is to broadcast per satellite a covariance matrix of residual errors through the message type 28. This matrix contains all the structure of the orbitography and synchronization residual errors. It can be seen as a protective ellipsoid around the computed satellite position and clock containing the true – but unknown – satellite position and clock at a certain level of confidence. Using the MT28 message each user is able to reconstruct the integrity value by projecting this protective ellipsoid along its line of sight. EGNOS operational system is implementing the MT27 solution whilst the WAAS is based on the MT28 one. The MT28 approach is the current baseline for EGNOS V3. Starting from recent R&D activities, Thales Alenia Space together with CNES (French Space Agency) has developed a dedicated module providing the message type 28 based on orbitography and fast synchronization variance-covariance matrices combined with satellites residual measurement errors. The MT28 formulation has been designed in collaboration with Statistics and Probabilities laboratories (Paris Descartes and Toulouse Paul Sabatier) in France. The algorithm contains also a mechanism that reacts immediately to orbit or clock satellite feared events such as a clock jump. This new concept for EGNOS provides a drastic improvement with respect to the first studies provided during EGNOS V3 phase A & B and HISTB V2 by the Thales consortium. The new MT28 module is integrated into a SPEED platform, the SBAS Operational Test-bed that fully represents EGNOS performances in terms of accuracy, continuity, availability and integrity for Safety Of Life services. The performance evaluation shows a very good level of EGNOS LPV200 availability with respect to the MT27 current approach. The integrity is constantly maintained on the Geostationary Broadcast Area with a good level of integrity margin. This paper provides a high level architecture description of this new EGNOS algorithm as well as a set of performance figures showing the achieved improvements