42 research outputs found
Gaussian stationary processes over graphs, general frame and maximum likelihood identification
In this paper, using spectral theory of Hilbertian operators, we study ARMA
Gaussian processes indexed by graphs. We extend Whittle maximum likelihood
estimation of the parameters for the corresponding spectral density and show
their asymptotic optimality
Adaptive Covariance Estimation with model selection
We provide in this paper a fully adaptive penalized procedure to select a
covariance among a collection of models observing i.i.d replications of the
process at fixed observation points. For this we generalize previous results of
Bigot and al. and propose to use a data driven penalty to obtain an oracle
inequality for the estimator. We prove that this method is an extension to the
matricial regression model of the work by Baraud
Stochastic Development Regression on Non-Linear Manifolds
We introduce a regression model for data on non-linear manifolds. The model
describes the relation between a set of manifold valued observations, such as
shapes of anatomical objects, and Euclidean explanatory variables. The approach
is based on stochastic development of Euclidean diffusion processes to the
manifold. Defining the data distribution as the transition distribution of the
mapped stochastic process, parameters of the model, the non-linear analogue of
design matrix and intercept, are found via maximum likelihood. The model is
intrinsically related to the geometry encoded in the connection of the
manifold. We propose an estimation procedure which applies the Laplace
approximation of the likelihood function. A simulation study of the performance
of the model is performed and the model is applied to a real dataset of Corpus
Callosum shapes
Non parametric estimation of the structural expectation of a stochastic increasing function
International audienceThis article introduces a non parametric warping model for functional data. When the outcome of an experiment is a sample of curves, data can be seen as realizations of a stochastic process, which takes into account the variations between the different observed curves. The aim of this work is to define a mean pattern which represents the main behaviour of the set of all the realizations. So, we define the structural expectation of the underlying stochastic function. Then, we provide empirical estimators of this structural expectation and of each individual warping function. Consistency and asymptotic normality for such estimators are proved
A Kriging procedure for processes indexed by graphs
International audienceWe provide a new kriging procedure of processes on graphs. Based on the construction of Gaussian random processes indexed by graphs, we extend to this framework the usual linear prediction method for spatial random fields, known as kriging. We provide the expression of the estimator of such a random field at unobserved locations as well as a control for the prediction error
Statistical M-Estimation and Consistency in Large Deformable Models for Image Warping
The problem of defining appropriate distances between shapes or images and modeling the variability of natural images by group transformations is at the heart of modern image analysis. A current trend is the study of probabilistic and statistical aspects of deformation models, and the development of consistent statistical procedure for the estimation of template images. In this paper, we consider a set of images randomly warped from a mean template which has to be recovered. For this, we define an appropriate statistical parametric model to generate random diffeomorphic deformations in two-dimensions. Then, we focus on the problem of estimating the mean pattern when the images are observed with noise. This problem is challenging both from a theoretical and a practical point of view. M-estimation theory enables us to build an estimator defined as a minimizer of a well-tailored empirical criterion. We prove the convergence of this estimator and propose a gradient descent algorithm to compute this M-estimator in practice. Simulations of template extraction and an application to image clustering and classification are also provided
Wavelet penalized likelihood estimation in generalized functional models
The paper deals with generalized functional regression. The aim is to
estimate the influence of covariates on observations, drawn from an exponential
distribution. The link considered has a semiparametric expression: if we are
interested in a functional influence of some covariates, we authorize others to
be modeled linearly. We thus consider a generalized partially linear regression
model with unknown regression coefficients and an unknown nonparametric
function. We present a maximum penalized likelihood procedure to estimate the
components of the model introducing penalty based wavelet estimators.
Asymptotic rates of the estimates of both the parametric and the nonparametric
part of the model are given and quasi-minimax optimality is obtained under
usual conditions in literature. We establish in particular that the LASSO
penalty leads to an adaptive estimation with respect to the regularity of the
estimated function. An algorithm based on backfitting and Fisher-scoring is
also proposed for implementation. Simulations are used to illustrate the finite
sample behaviour, including a comparison with kernel and splines based methods