Contributions in infinite-dimensional statistics and related topics

Bongiorno, Enea G.; Salinelli, Ernesto; Goia, Aldo; Vieu, Philippe

doi:10.15651/9788874887637

Cited by 57 publications

(35 citation statements)

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“…We thank Jeff Palmer for reviewing the English of the manuscript. Part of this work was presented to the 3rd IWFOS Conference in Stresa, June 2014 (see Bongiorno et al, 2014).…”

Section: Acknowledgementsmentioning

confidence: 99%

Optimal level sets for bivariate density representation

Delicado

Vieu

2015

Journal of Multivariate Analysis

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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 one wishes to highlight in the density, the answer to which requires both the definition of what the optimal level is and the construction of a method for finding it. We consider two scenarios for this problem. The first one corresponds to situations in which one has just a single density function to be represented. However, as a result of the technical progress in data collecting, problems are emerging in which one has to deal with a sample of densities. In these situations, the need arises to develop joint representation for all these densities, and this is the second scenario considered in this paper. For each case, we provide consistency results for the estimated levels and present wide Monte Carlo simulated experiments illustrating the interest and feasibility of the proposed method.

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“…We thank Jeff Palmer for reviewing the English of the manuscript. Part of this work was presented to the 3rd IWFOS Conference in Stresa, June 2014 (see Bongiorno et al, 2014).…”

Section: Acknowledgementsmentioning

confidence: 99%

Optimal level sets for bivariate density representation

Delicado

Vieu

2015

Journal of Multivariate Analysis

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“…Such data are known in the literature as functional data (Bongiorno et al 2014;Ferraty and Vieu 2006;Horváth and Kokoszka 2012;Ramsay and Silverman 2005). Examples of functional data can be found in various application domains, such as medicine, economics, meteorology and many others.…”

Section: Introductionmentioning

confidence: 99%

Selected statistical methods of data analysis for multivariate functional data

et al. 2016

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Data in the form of a continuous vector function on a given interval are referred to as multivariate functional data. These data are treated as realizations of multivariate random processes. The paper is devoted to three statistical dimension reduction techniques for multivariate data. For the first one, principal components analysis, the authors present a review of a recent paper (Jacques and Preda in, Comput Stat Data Anal, 71:92-106, 2014). For two others one, canonical variables and discriminant coordinates, the authors extend existing works for univariate functional data to multivariate. These methods for multivariate functional data are presented, illustrated and discussed in the context of analyzing real data sets. Each of these techniques is applied on real data set.

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“…In such perspective, our work can be included in the front of literature on selection variable, rather than only in the semi-parametric regression context. In that sense, our paper can be seen as taking part on the recent advances devoted to explore links between Functional Data Analysis and Variable Selection Procedures (see for instance Bongiorno et al 2014). …”

Section: Discussionmentioning

confidence: 99%

A partitioned Single Functional Index Model

Goia

Vieu

2014

Comput Stat

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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 real curves datasets. It appears, from an example of interest in spectrometry, that the method provides a nice exploratory tool both for analyzing structural changes in the spectrum and for visualizing the most informative directions, still keeping good predictive power. Even if the main objective of this work is to discuss applied issues of the method, asymptotic behaviour is shortly described.

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Contributions in infinite-dimensional statistics and related topics

Cited by 57 publications

References 0 publications

Optimal level sets for bivariate density representation

Optimal level sets for bivariate density representation

Selected statistical methods of data analysis for multivariate functional data

A partitioned Single Functional Index Model

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