Fabrice Gamboa

Large deviations for quadratic forms of stationary Gaussian processes

A large deviation principle is proved for Toeplitz quadratic forms of centred stationary Gaussian processes. The rate function is obtained by a sharp study of the behaviour of eigenvalues of a product of two Toeplitz matrices. Some statistical applications such as the likelihood ratio test and the estimation of the parameter of an autoregressive Gaussian process are also provided.

Local Polynomial Estimation for Sensitivity Analysis on Models With Correlated Inputs

Sensitivity indexes when the inputs of a model are not independent are derived from local polynomial techniques. Two original estimators based on local polynomial smoothers are proposed. Both have good theoretical properties, which are illustrated through analytical examples. Comparison with the Bayesian approach developed by Oakley and O’Hagan (2004) is also performed. The two proposed estimators are used to carry out a sensitivity analysis on two real case models with correlated parameters.

Semi-parametric estimation of shifts

We observe a large number of functions differing from each other only by a translation parameter. While the main pattern is unknown, we propose to estimate the shift parameters using

Generalized Hoeffding-Sobol Decomposition for Dependent Variables - Application to Sensitivity Analysis

M

Source separation when the input sources are discrete or have constant modulus

-estimators. Fourier transform enables to transform this statistical problem into a semi-parametric framework. We study the convergence of the estimator and provide its asymptotic behavior. Moreover, we use the method in the applied case of velocity curve forecasting.

MEM pixel correlated solutions for generalized moment and interpolation problems

In this paper, we consider a regression model built on dependent variables. This regression modelizes an input output relationship. Under boundedness assumptions on the joint distribution function of the input variables, we show that a generalized Hoeffding-Sobol decomposition is available. This leads to new indices measuring the sensitivity of the output with respect to the input variables. We also study and discuss the estimation of these new indices.

Estimation of Translation, Rotation, and Scaling between Noisy Images Using the Fourier-Mellin Transform

In this paper, we present a new method for the source separation problem when some prior information on the input sources is available. More specifically, we study the situation where the distributions of the input signals are discrete or are concentrated on a circle. The method is based on easy properties of Hankel forms and on the divisibility of Gaussian distributions. In both situations, we prove that the estimator converges in absence of noise or if we know the first moments of the noise up to its scale. Moreover, in the absence of noise, the estimate converges with a finite number of observations.

A functional large deviations principle for quadratic forms of Gaussian stationary processes

In generalized moment problems (signed) measures are searched to fit given observations, or continuous functions are searched to fit given constraints. Known convex methods for solving such problems, and their stochastic interpretations via maximum entropy on the mean (MEM) and in a Bayesian sense are reviewed, with some improvements on previous results. Then the MEM and Bayesian approaches are extended to default models with a dependence structure, yielding new families of solutions. One family involves a transfer kernel, and allows using prior information such as modality, convexity, or Sobolev norms. Another family of solutions with possibly nonconvex criteria, is arrived at using default models with exchangeable random variables. The main technical tools are convex analysis and large deviations theory.

Generalized Sobol sensitivity indices for dependent variables: numerical methods

In this paper we focus on extended Euclidean registration of a set of noisy images. We provide an appropriate statistical model for this kind of registration problem, and a new criterion based on Fourier-type transforms is proposed to estimate the translation, rotation, and scaling parameters to align a set of images. This criterion is a two-step procedure which does not require the use of a reference template onto which all the images are aligned. Our approach is based on

Large Deviations for random power moment problem

M