65 research outputs found
Robust Estimation and Wavelet Thresholding in Partial Linear Models
This paper is concerned with a semiparametric partially linear regression
model with unknown regression coefficients, an unknown nonparametric function
for the non-linear component, and unobservable Gaussian distributed random
errors. We present a wavelet thresholding based estimation procedure to
estimate the components of the partial linear model by establishing a
connection between an -penalty based wavelet estimator of the
nonparametric component and Huber's M-estimation of a standard linear model
with outliers. Some general results on the large sample properties of the
estimates of both the parametric and the nonparametric part of the model are
established. Simulations and a real example are used to illustrate the general
results and to compare the proposed methodology with other methods available in
the recent literature
Classification of EEG recordings in auditory brain activity via a logistic functional linear regression model
We want to analyse EEG recordings in order to investigate the phonemic
categorization at a very early stage of auditory processing. This problem can
be modelled by a supervised classification of functional data. Discrimination
is explored via a logistic functional linear model, using a wavelet
representation of the data. Different procedures are investigated, based on
penalized likelihood and principal component reduction or partial least squares
reduction
Estimation par ondelettes dans des modèles fonctionnels généralisés
National audienceL'estimation par ondelettes de signaux en présence de bruit gaussien a été largement développée ces dernières années. Le but de ce travail est d'étendre les résultats à des contextes faisant appel à des distributions plus générales telles que Poisson, Binomiale ou Gamma... Nous considérons une approche par log-vraisemblance pénalisée, où la pénalité s'exprime à l'aide des coefficients d'ondelettes. Nous nous intéressons par ailleurs au cas où un terme linéaire est estimé simultanément. Nous montrons l'optimalité asymptotique de la procédure d'estimation et nous proposons un algorithme simple de mise en oeuvre
Wavelet-Based and Fourier-Based Multivariate Whittle Estimation: multiwave
Multivariate time series with long-dependence are observed in many applications such as finance, geophysics or neuroscience. Many packages provide estimation tools for univariate settings but few are addressing the problem of long-dependence estimation for multivariate settings. The package multiwave is providing efficient estimation procedures for multivariate time series. Two semi-parametric estimation methods of the long-memory exponents and long-run covariance matrix of time series are implemented. The first one is the Fourier-based estimation proposed by Shimotsu (2007) and the second one is a wavelet-based estimation described in Achard and Gannaz (2016). The objective of this paper is to provide an overview of the R package multiwave with its practical application perspectives
Adaptive density estimation under dependence
Assume that is a real valued time series admitting a common
marginal density with respect to Lebesgue's measure. Donoho {\it et al.}
(1996) propose a near-minimax method based on thresholding wavelets to estimate
on a compact set in an independent and identically distributed setting. The
aim of the present work is to extend these results to general weak dependent
contexts. Weak dependence assumptions are expressed as decreasing bounds of
covariance terms and are detailed for different examples. The threshold levels
in estimators depend on weak dependence properties of the
sequence through the constant. If these properties are
unknown, we propose cross-validation procedures to get new estimators. These
procedures are illustrated via simulations of dynamical systems and non causal
infinite moving averages. We also discuss the efficiency of our estimators with
respect to the decrease of covariances bounds
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
Ondelettes et modèles partiellement lineaires généralisés.
National audienceLes modèles partiellement linéaires distinguent dans un signal des relations linéaires et des relations fonctionnelles, non paramétriques
Estimation par ondelettes dans les modèles partiellement linéaires
PosterNational audienc
Inference of dependence graphs by multiple testing, with application to brain connectivity
International audienc
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