About
221
Publications
27,477
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
10,083
Citations
Publications
Publications (221)
This paper focuses on a semi-parametric regression model in which the response variable is explained by the sum of two components. One of them is parametric (linear), the corresponding explanatory variable is measured with additive error and its dimension is finite (p). The other component models, in a nonparametric way, the effect of a functional...
In this paper, we focus on the studying of composite quantile estimation for the partially functional linear regression model with randomly censored responses. Concretely, we adopt the approach of inverse probability weighting to estimate the weights by using the survival distribution function of the censoring variables with the methods of Kaplan–M...
We study the non-parametric estimation of partially linear generalized single-index functional models, where the systematic component of the model has a flexible functional semi-parametric form with a general link function. We suggest an efficient and practical approach to estimate (I) the single-index link function, (II) the single-index coefficie...
In this paper, we first investigate the estimation of the functional single index regression model with missing responses at random for strong mixing time series data. More precisely, the uniform almost complete convergence rate and asymptotic normality of the estimator are obtained respectively under some general conditions. Then, some simulation...
A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a single‐index structure, while the other is included linearly through the high‐dimensional vector formed by its discreti...
This paper aims to present the various contributions to the Special Issue of the Journal of Multivariate Analysis on Functional Data Analysis and some related topics including High-Dimensional Statistics and Multivariate Analysis of complex data. The presentation is made by emphasizing on how the contributions are behaving among recent trends in th...
Despite of various similar features, Functional Data Analysis and High-Dimensional Data Analysis are two major fields in Statistics that grew up recently almost independently one from each other. The aim of this paper is to propose a survey on methodological advances for variable selection in functional regression, which is typically a question for...
Single-index models are potentially important tools for multivariate nonparametric regression analysis. They generalize linear regression models by replacing the linear combination $\alpha_0^T X$ with a nonparametric component $\eta_0\left(\alpha_0^T X\right)$, where $\eta_0(\cdot)$ is an unknown univariate link function. Wang and Cao (2018) studie...
A fast and flexible kNN procedure is developed for dealing with a semiparametric functional regression model involving both partial-linear and single-index components. Rates of uniform consistency are presented. Simulated experiments highlight the advantages of the kNN procedure. A real data analysis is also shown.
The aim of this paper is to provide a selected advanced review on semiparametric regression which is an emergent promising field of researches in functional data analysis. As a deliberate strategy, we decided to focus our discussion on the single functional index regression (SFIR) model in order to fix the ideas about the stakes linked with infinit...
We investigate kernel estimates in the functional nonparametric regression model when both the response and the explanatory variable (the covariate) are functional. The rates of almost complete and uniform almost complete convergence of the estimator are obtained under some mild α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysy...
This paper aims to front with dimensionality reduction in regression setting when the predictors are a mixture of functional variable and high-dimensional vector. A flexible model, combining both sparse linear ideas together with semiparametrics, is proposed. A wide scope of asymptotic results is provided: this covers as well rates of convergence o...
This volume is composed by a set of short papers corresponding to some of the contributions that were sent to be presented at the fifth edition of the International Workshop on Functional and Operatorial Statistics (IWFOS). This fifth edition was to be held in June 2020 in Brno (Czech Republic), but had to be postponed as a consequence of the healt...
A new sparse semiparametric functional model is proposed, which tries to incorporate the influence of two functional variables in a scalar response in a flexible way, but involving interpretable parameters. One of the functional variables is included trough a single-index structure and the other one linearly, but trough the high-dimensional vector...
This contribution deals with the estimation of the functional single index regression model (FSIRM) with responses missing at random (MAR) for strong mixing time series data. Some asymptotic properties such as the uniform almost complete convergence rate and asymptotic normality of the estimator are obtained respectively under some general conditio...
The Small-Ball Probability (SmBP) of a process valued in a semi-metric space is considered. Assume that it factorizes in two terms that play the role of a surrogate density and of a volumetric term, respectively. This work presents some recent developments concerning the study of the volumetric term that detains information about the complexity of...
A statistical procedure combining the local adaptivity and the easiness of implementation of k-nearest-neighbours (kNN) estimates together with the semiparametric flexibility of partial linear modeling is developed for regression problems involving functional variable. Various asymptotic results are stated, both for the linear parameters and for th...
Consider a random curve valued in a general semi-metric space whose small-ball probability factorizes isolating the spatial and the volumetric term. Assume that the latter is specified and interprets its parameters as complexity indexes. An index estimate is constructed by comparing nonparametric versus parametric estimates of the volumetric factor...
This book presents the latest research on the statistical analysis of functional, high-dimensional and other complex data, addressing methodological and computational aspects, as well as real-world applications. It covers topics like classification, confidence bands, density estimation, depth, diagnostic tests, dimension reduction, estimation on ma...
A new sparse semiparametric functional model is proposed, which tries to incorporate the influence of two functional variables in a scalar response in a quite simple and interpretable way. One of the functional variables is included trough a single-index structure and the other one linearly, but trough the high-dimensional vector of its discretized...
The paper deals with a test procedure able to state the compatibility of observed data with a reference model, by using an estimate of the volumetric part in the small-ball probability factorization which plays the role of a real complexity index. As a preliminary by-product we state some asymptotics for a new estimator of the complexity index. A s...
In the context of nuclear safety experiments, we consider curves issued from acoustic emission. The aim of their analysis is the forecast of the physical phenomena associated with the behavior of the nuclear fuel. In order to cope with the complexity of the signals and the diversity of the potential source mechanisms, we experiment innovative clust...
In this paper, we investigate the k-nearest neighbours (kNN) estimation of nonparametric regression model for strong mixing functional time series data. More precisely, we establish the uniform almost complete convergence rate of the kNN estimator under some mild conditions. Furthermore, a simulation study and an empirical application to the real d...
This paper develops a new automatic and location-adaptive procedure for estimating regression in a Functional Single-Index Model (FSIM). This procedure is based on k-Nearest Neighbours (kNN) ideas. The asymptotic study includes results for automatically data-driven selected number of neighbours, making the procedure directly usable in practice. The...
This paper focuses on semi-functional partially linear regression model, where a scalar response variable with missing at random is explained by a sum of an unknown linear combination of the components of multivariate random variables and an unknown transformation of a functional random variable which takes its value in a semi-metric abstract space...
This paper provides a structured overview of the contents of this Special Issue of the Journal of Multivariate Analysis devoted to Functional Data Analysis and Related Topics, along with a brief survey of the field.
The variable selection problem is studied in the sparse semi-functional partial linear model, with single-index type influence of the functional covariate in the response. The penalized least squares procedure is employed for this task. Some properties of the resultant estimators are derived: the existence (and rate of convergence) of a consistent...
Nonparametric functional data analysis is a field whose development started some 15 years ago and there is a very extensive literature on the topic (hundreds of papers published now). The first aim of this survey is to discuss the state of art in the field through a necessarily selected, bibliographical survey. The second aim is to present a wide s...
In this paper we study the complexity of a functional data set drawn from particular processes by means of a two-step approach. The first step considers a new graphical tool for assessing to which family the data belong: the main aim is to detect whether a sample comes from a monomial or an exponential family. This first tool is based on a nonparam...
Prior to an effective interpretation of AE signals in noisy nuclear environment, it is necessary to define an
appropriate strategy for detecting structural changes and denoising signals, according to the stochastic behavior of the noise and its level. The ability and efficiency of various methods are studied here. One conclusion of this work is tha...
This paper deals with the semi-functional partial linear regression model \(Y={{\varvec{X}}}^\mathrm{T}{\varvec{\beta }}+m({\varvec{\chi }})+\varepsilon \) under \(\alpha \)-mixing conditions. \({\varvec{\beta }} \in \mathbb {R}^{p}\) and \(m(\cdot )\) denote an unknown vector and an unknown smooth real-valued operator, respectively. The covariates...
When exploring a sample composed with a set of bivariate density functions, the question of the visualisation of the data has to front with the choice of the relevant level set(s). The approach proposed in this paper consists in defining the optimal level set(s) as being the one(s) allowing for the best reconstitution of the whole density. A fully...
In a context of nuclear Reactivity Initiated Accident, we describe acoustic emission signals, for which a problem of classification is open. As classical approaches with a reduced number of variables do not give satisfactory discrimination, we propose to use the envelopes of the received signals. We perform a k-means clustering and discuss the firs...
This presentation aims to introduce an approach for dealing with sparse regression models when functional variables are involved in the statistical sample. The idea is not to restrict to any specific variable selection procedure, but rather to present a two-stage methodology allowing to adapt efficiently any multivariate procedure to the functional...
This contribution deals with functional conditional mode estimation given a functional explanatory variable with both stationary ergodic and responses missing at random (MAR). More precisely, we propose the estimators for functional conditional density and conditional mode respectively in this case. The main results of the work are the establishmen...
This paper focuses on uniform in bandwidth and uniform in nearest neighbors consistencies of both kernel and kNN type estimators involving functional data. We established in previous works results in this topic for a selection of nonparametric conditional operators. Our interest here is to adapt that approach for studying the generalized nonparamet...
Semi-functional partial linear regression model allows to deal with a nonparametric and a linear component within the functional regression. Naïve and wild bootstrap procedures are proposed to approximate the distribution of the estimators for each component in the model, and their asymptotic validities are obtained in the context of dependence dat...
The aim of this introductory chapter is to present the various contributions to the fourth edition of the International Workshop on Functional and Operatorial Statistics (IWFOS 2017) held in June 2017 in A Coruña, Spain. These contributions are put into the context of the recent developments on Functional Data Analysis and related fields.
The Geometric Brownian Motion type process is commonly used to describe stock price movements and is basic for many option pricing models. In this paper a new methodology for recognizing Brownian functionals is applied to financial datasets in order to evaluate the compatibility between real financial data and the above modeling assumption. The met...
This volume collects latest methodological and applied contributions on functional, high-dimensional and other complex data, related statistical models and tools as well as on operator-based statistics. It contains selected and refereed contributions presented at the Fourth International Workshop on Functional and Operatorial Statistics (IWFOS 2017...
This paper proposes a fully nonparametric model for regression problems involving an infinite-dimensional covariate in which sparsity is modelled in an additive way. The continuous nature of the variable allows to develop new variable selection procedures. Theoretical results show the improvement, in terms of both rate of convergence and number
of...
Dans un problème de régression avec variable explicative fonctionnelle, on s'intéresse à la sélection des points les plus informatifs. Un modèle parcimonieux de type non paramétrique ainsi qu'une procédure de choix de variables basée sur une pré-sélection par dépistage sont proposés, et des résultats asymptotiques sont établis concernant à la fois...
In this paper, we investigate the asymptotic properties of a non-parametric conditional mode estimation given a functional explanatory variable, when functional stationary ergodic data and missing at random responses are observed. First of all, we establish asymptotic properties for a conditional density estimator from which we derive almost sure c...
This paper considers naive and wild bootstrap procedures to construct pointwise confidence intervals for a nonparametric regression function when the predictor is of functional nature and when the data are dependent. Assuming α-mixing conditions on the sample, the asymptotic validity of both procedures is obtained. A simulation study shows promisin...
The aim of this short contribution is to present the various papers composing this Special Issue on Statistics in HD spaces, by putting them back into their bibliographical context through some necessarily short and selected discussion of the current literature.
This paper focuses on partially linear regression models with several real and functional covariates. The aim is to construct an estimate of the variance of the error. In our model, a real-valued response variable is explained by the sum of an unknown linear combination of the components of a multivariate random variable and an unknown transformati...
In bivariate density representation there is an extensive literature on level set estimation when the level is fixed, but this is not so much the case when choosing which level is (or which levels are) of most interest. This is an important practical question which depends on the kind of problem one has to deal with as well as the kind of feature o...
This paper takes part on the current literature on semi-parametric regression modelling for statistical samples composed of multi-functional data. A new kind of partially linear model (so-called MFPLR model) is proposed. It allows for more than one functional covariate, for incorporating as well continuous and discrete effects of functional variabl...
In this paper, we investigate the asymptotic properties of the estimator for the regression function operator whenever the functional stationary ergodic data with missing at random (MAR) are considered. Concretely, we construct the kernel type estimator of the regression operator for functional stationary ergodic data with the responses MAR, and so...
The problem of variable selection is considered in high-dimensional partial linear regression under some model allowing for possibly functional variable. The procedure studied is that of nonconcave-penalized least squares. It is shown the existence of a √n/sn-consistent estimator for the vector of pn linear parameters in the model, even when pn ten...
This paper is on regression models when the explanatory variable is a function. The question is to look for which among the pnpn discretized values of the function must be incorporated in the model. The aim of the paper is to show how the continuous structure of the data allows to develop new specific variable selection procedures, which improve th...
One of the current challenge proposed to the nonparametric community is to deal with high dimensional (and possibly infinite dimensional) data. In high (but finite) dimensional setting the key question is often to proceed to some variable selection stage. In the infinite framework, which involves the so-called functional data, an usual approach con...
We consider the problem of short-term peak load forecasting in a district-heating system using past heating demand data. Taking advantage of the functional nature of the data, we introduce a forecasting methodology based on functional regression approach. To avoid the limitations due to the linear specification when one uses the linear model and to...
This paper discusses the problem of testing misspecifications in semiparametric regression models for a large family of econometric models under rather general conditions. We focus on two main issues that typically arise in econometrics. First, many econometric models are estimated through maximum likelihood or pseudo-ML methods like, for example,...
Given a functional regression model with scalar response, the aim is to present a methodology in order to approximate in a semi-parametric way the unknown regression operator through a single index approach, but taking possible structural changes into account. Our paper presents this methodology and illustrates its behaviour both on simulated and r...
The objective of this article is to assess the relevance of a statistical method for hyperspectral image classification. We focus on the implementation of a functional method whose main objective is to consider each hyperspectrum as a continuous curve in order to predict its associated class. The implemented functional nonparametric discrimination...
The objective of this article is to assess the relevance of a statistical method for hyperspectral image classification. We focus on the implementation of a functional method whose main objective is to consider each hyperspec-trum as a continuous curve in order to predict its associated class. The implemented functional nonparametric discrimination...
This paper is devoted to nonparametric analysis of functional data. We give asymptotic results for a kkNN generalized regression estimator when the observed variables take values in any abstract space. The main novelty is our uniform consistency result (with rates).
In this paper we introduce a flexible approach to approximate the regression function in the case of a functional predictor and a scalar response. Following the Projection Pursuit Regression principle, we derive an additive decomposition which exploits the most interesting projections of the prediction variable to explain the response. On one hand,...
This paper investigates a semi-parametric model for functional data, based on partial linear ideas. A methodology is developped for testing the linear component of such a functional partial linear model. The behavior of the test is studied through some finite simulated samples before being applied to some chemometrical curves dataset. One interesti...
We consider a nonparametric regression model where the response Y and the covariate X are both functional (i.e. valued in some infinite-dimensional space). We define a kernel type estimator of the regression operator and we first establish its pointwise asymptotic normality. The double functional feature of the problem makes the formulas of the asy...
We consider a kernel estimate of the regression when the response variable is in a Banach space and the explanatory variable takes its values in a semi-metric space. Our main result states the almost complete convergence (with rate) of the constructed estimate when the sample considered is a β-mixing sequence.
A density function is generally not well defined in functional data context, but we can define a surrogate of a probability density, also called pseudo-density, when the small ball probability can be approximated by the product of two independent functions, one depending only on the centre of the ball. The aim of this paper is to study two kernel m...
In this paper we construct a statistic to test a specific form of the conditional density function. The main point of this work is to consider a functional explanatory variable, and the statistic is constructed following recent advances in nonparametric functional data analysis. The asymptotic behavior of the test statistic is studied under both th...
IntroductionThe Nadaraya–Watson Kernel Regression EstimatePointwise Bias Properties of the Nadaraya–Watson EstimatePointwise Variance Properties of the Nadaraya–Watson EstimateTrade-off Between Bias and Variance: The Mean Squared ErrorGlobal Results: Mean Integrated Squared Error PropertiesL∞ Convergence Properties of the Nadaraya–Watson EstimateCo...
In a missing-data setting, we want to estimate the mean of a scalar outcome, based on a sample in which an explanatory variable is observed for every subject while responses are missing by happenstance for some of them. We consider two kinds of estimates of the mean response when the explanatory variable is functional. One is based on the average o...
In this paper, we consider the functional linear model with scalar response, and explanatory variable valued in a function space. In recent literature, functional principal components analysis (FPCA) has been used to estimate the model parameter. We propose to modify this approach by using presmoothing techniques. For this new estimate, consistency...
Partial linear modelling ideas have recently been adapted to situations when functional data are observed. This paper aims
to complete the study of such model by proposing a fully automatic estimation procedure. This is achieved by constructing
a data-driven method to choose the smoothing parameters entered in the nonparametric components of the mo...
There is no single method available for estimating the seismic risk in a given area, and as a result most studies are based
on some statistical model. If we denote by Z the random variable that measures the maximum magnitude of earthquakes per unit time, the seismic risk of a value m is the probability that this value will be exceeded in the next t...
We deal with a regression model where a functional covariate enters in
a nonparametric way, a divergent number of scalar covariates enter in a linear way
and the corresponding vector of regression coefficients is sparse. A penalized-leastsquares
based procedure to simultaneously select variables and estimate regression
coefficients is proposed, and...
We present some recent results about nonparametric conditional density estimation, when we consider a functional explanatory
variable, and some applications of these techniques to econometrics. In a first part, we construct a test to check the parametric
form of the conditional density function. In a second part, we estimate two well-known risk mea...
We introduce a flexible approach to approximate the regression function in the case of a functional predictor and a scalar
response. Following the Projection Pursuit Regression principle, we derive an additive decomposition which exploits the most
interesting projections of the prediction variable to explain the response. The goodness of our proced...
In this work, we have focused on the nonparametric regression model with scalar response and functional covariate, and we
have analyzed the existence of underlying complex structures in data by means of a thresholding procedure. Several thresholding
functions are proposed, and a cross-validation criterion is used in order to estimate the threshold...
Many papers deal with structural testing procedures in multivariate regression. More recently, various estimators have been proposed for regression models involving functional explanatory variables. Thanks to these new estimators, we propose a theoretical framework for structural testing procedures adapted to functional regression. The procedures i...
Résumé Les progrés récents enmatì ere de stockage et de traitement des données se traduisent de plus en plus fréquemment dans de nombreux domaines scienti-fiques par la présence de données de type fonctionnel (courbes, images, ...). Les défis proposés aux statisticiens pour appréhender ce type de données ont abouti depuis quelques année a la constr...
This work focuses on recent advances on the way general structural testing procedures can be constructed in regression on
functional variable. Our test statistic is constructed from an estimator adapted to the specific model to be checked and uses
recent advances concerning kernel smoothing methods for functional data. A general theoretical result...
We consider kernel regression estimate when both the response variable and the explanatory one are functional. The rates of uniform almost complete convergence are stated as function of the small ball probability of the predictor and as function of the entropy of the set on which uniformity is obtained.
Frédéric Ferraty, Pascal Sarda, and Philippe Vieu are three researchers in Statistics at Toulouse University (France). They have been working on all facets of Statistics, ranging from fundamental theory basis, methodology developments to practical implementation. In addition, most of major topics of Statistics as Classification, Exploratory Methods...
We suggest a way of reducing the very high dimension of a functional predictor, X, to a low number of dimensions chosen so as to give the best predictive performance. Specifically, if X is observed on a fine grid of design points t<sub>1</sub>,…, t<sub>r</sub>, we propose a method for choosing a small subset of these, say t<sub>i<sub>1</sub></sub>,...
The general framework of this paper deals with the nonparametric regression of a scalar response on a functional variable (i.e. one observation can be a curve, surface, or any other object lying into an infinite-dimensional space). This paper proposes to model local behaviour of the regression operator (i.e. the link between a scalar response and a...
We consider the functional non-parametric regression model "Y"= "r"( "χ" )+"ϵ", where the response "Y" is univariate, "χ" is a functional covariate (i.e. valued in some infinite-dimensional space), and the error "ϵ" satisfies "E"("ϵ" | "χ" ) = 0. For this model, the pointwise asymptotic normality of a kernel es...
In this paper we investigate nonparametric estimation of some functionals of the conditional distribution of a scalar response variable Y given a random variable X taking values in a semi-metric space. These functionals include the regression function, the conditional cumulative distribution, the conditional density and some other ones. The literat...
Le dépistage actuel du cancer broncho-pulmonaire est effectué à l'aide d'une radiographie pulmonaire, d'un scanner thoracique et d'un examen cytologique des expectorations. La cytologie automatisée des expectorations est une méthode permettant l'analyse informatique des cellules d'un crachat sur la lame d'un microscope. Comme une personne est repré...
Ce travail s'intéresse à la construction et à l'utilisation de tests de structure en régression sur variable fonctionnelle. Nous proposons, de manière générale, de construire notre statistique de test à partir d'un estimateur spécifique au modèle particulier dont nous voulons tester la validité et de méthodes d'estimation à noyau fonctionnel. Un ré...
The aim of this article is to study the k-nearest neighbour (kNN) method in nonparametric functional regression. We present asymptotic properties of the kNN kernel estimator: the almost-complete convergence and its rate. Then, we illustrate the effectiveness of this method by comparing it with the traditional kernel approach first on simulated data...
Additive model and estimates for regression problems involving functional data are proposed. The impact of the additive methodology for analyzing datasets involving various functional covariates is underlined by comparing its predictive power with those of standard (i.e. non additive) nonparametric functional regression methods. The comparison is m...