Functional and High-Dimensional Statistics and Related Fields

270 Pages·2020·8.702 MB·English

by  Germán Aneiros, Ivana Horová, Marie Hušková, Philippe Vieu

Contributions to Statistics
Germán Aneiros
Ivana Horová
Marie Hušková
Philippe Vieu  Editors
Functional and
High-Dimensional
Statistics and
Related Fields
Contributions to Statistics
The series Contributions to Statistics contains publications in theoretical and
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More information about this series at http://www.springer.com/series/2912
Germán Aneiros • Ivana Horová
Marie Hušková • Philippe Vieu
Editors
Functional
and High-Dimensional
Statistics and Related Fields

123
Editors
Germán Aneiros Ivana Horová
Department of Mathematics Department of Mathematics
University of A Coruña and Statistics
A Coruña, Spain Masaryk University
B rno, Czech Republic
Marie Hušková
Department of Probability Philippe Vieu
and Mathematical Statistics Toulouse Mathematics Institute
Charles University Paul Sabatier University - Toulouse III
Prague, Czech Republic Toulouse, France
ISSN 1431-1968
Contributions to Statistics
ISBN 978-3-030-47755-4 ISBN 978-3-030-47756-1 (eBook)
https://doi.org/10.1007/978-3-030-47756-1

Mathematics Subject Classification (2020): 62-07, 62G05, 62G09, 62G20, 62F12, 62F15, 62F40, 62H25

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Preface
During the last twelve years, the International Workshop on Functional and Op-
eratorial Statistics has become a prominent platform for exchange of ideas and
communicationinthegrowingcommunityofresearchersinfunctionaldataanaly-
sis.FollowingthesuccessofthepreviousmeetingsheldinToulouse(France,2008),
Santander (Spain, 2011), Stresa (Italy, 2014) and A Coruña (Spain, 2017), the 5th
IWFOStakesplaceatMasarykUniversityinBrno,CzechRepublic.Theworkshop
was originally planned for June 2020 but due to the rapidly evolving coronavirus
pandemicithasbeenpostponed.Nevertheless,thiscollectionofpeer-reviewedshort
papersispublishedasplanned.Itreflectsthediversityoftheoretical,methodological
andappliedadvancesinfunctionaldataanalysisanditsintersectionwithotherareas
ofstatistics,suchashigh-dimensionaldataanalysisandnonparametricstatistics,as
wellasthediversityofthecommunityitself.
We would like to thank all the authors presenting their work at the workshop.
We are particularly grateful to invited speakers Gérard Biau (Sorbonne Univer-
sité,France),EduardoGarcíaPortugués(UniversidadCarlosIIIdeMadrid,Spain),
Lajos Horváth (University of Utah, USA), Roberto Imbuzeiro (Instituto Nacional
de Matemática Pura e Aplicada, Brazil), Dominik Liebl (Rheinische Friedrich-
Wilhelms-Universität Bonn, Germany), Regina Y. Liu (Rutgers School of Arts
and Sciences, USA), Stanislav Nagy (Charles University, Prague, Czech Repub-
lic),PiercesareSecchi(PolitecnicodiMilano,Italy)andYoavZemel(Universityof
Cambridge,UnitedKingdom).
WeespeciallyappreciatetheeffortofthemembersoftheScientificCommittee,
namely John Aston (Cambridge, UK), Ricardo Cao (A Coruña, Spain), Antonio
Cuevas (Madrid, Spain), Aurore Delaigle (Melbourne, Australia), Manuel Febrero
(Santiago de Compostela, Spain), Ricardo Fraiman (Montevideo, Uruguay), Aldo
Goia (Novara, Italy), Daniel Hlubinka (Prague, Czech Republic), Siegfried Hör-
mann (Graz, Austria), David Kraus (Brno, Czech Republic), Sara Lopez-Pintado
(NewYork,USA),SteveMarron(ChapelHill,USA),AlexanderMeister(Rostock,
Germany),VictorPanaretos(Lausanne,Switzerland),GregRice(Waterloo,Canada)
v
vi Preface
and Simone Vantini (Milan, Italy), and other experts during the preparation of the
scientificprogramandthereviewprocess.
We are grateful to the following academic and private institutions and organi-
zations for their support: Faculty of Science, Masaryk University, Brno, Faculty
of Mathematics and Physics, Charles University, Prague, Union of Czech Math-
ematicians and Physicists, Brno branch, Institut de Mathématiques de Toulouse,
Autocont,PrefaBrno,Kiwi.com,TrilobyteStatisticalSoftware,SC&CPartnerand
HomeCredit.
ThepreparationofIWFOSispossiblethankstothemembersoftheOrganizing
Committee,inparticular,EneaBongiorno,MarieBudíková,JitkaForejtováZhořová,
Jan Koláček, Zdeněk Pospíšil, Lenka Přibylová, Petr Vitík and Jan Vondra. The
preparation of the proceedings went smoothly thanks to the dedicated work of
OndřejPokora,JiříZelinkaandDavidKrausfromtheOrganizingCommittee,and
VeronikaRosteckandGerlindeSchusterofSpringer.
Brno,March2020 GermánAneiros
IvanaHorová
MarieHušková
PhilippeVieu
Contents
Preface ....................................................... v
ListofContributors ............................................ xv
1 Anintroductiontothe(postponed)5theditionoftheInternational
WorkshoponFunctionalandOperatorialStatistics .............. 1
GermánAneiros,IvanaHorová,MarieHuškováandPhilippeVieu
1.1 IWFOSandFunctionalDataAnalysis ........................ 1
1.2 Presentationofthevariouschapters .......................... 2
References ..................................................... 4
2 Analysis of Telecom Italia Mobile Phone Data by Space-time
RegressionwithDifferentialRegularization ..................... 5
EleonoraArnone,MaraS.Bernardi,LauraM.SangalliandPiercesare
Secchi
2.1 Space-TimeRegressionwithDifferentialRegularization......... 5
2.2 TelecomItaliaMobilePhoneData ........................... 6
2.3 ST-PDEModelandEstimatingtheNon-stationaryAnisotropy.... 8
References ..................................................... 9
3 SomeNumericalTestontheConvergenceRatesofRegressionwith
DifferentialRegularization ................................... 11
EleonoraArnone,AloisKneip,FabioNobileandLauraM.Sangalli
3.1 Introduction.............................................. 11
3.2 SpatialRegressionwithPDEPenalization..................... 12
3.3 NumericalStudyofAsymptoticProperties .................... 14
3.4 FutureDirections ......................................... 16
References ..................................................... 17
vii
viii Contents
4 LearningwithSignatures .................................... 19
GérardBiauandAdelineFermanian
4.1 Introduction.............................................. 19
4.2 SignatureDefinitionandFirstProperties...................... 21
4.3 Embeddings.............................................. 23
References ..................................................... 26
5 About the Complexity Function in Small-ball Probability
Factorization .............................................. 27
EneaG.Bongiorno,AldoGoiaandPhilippeVieu
5.1 Introduction.............................................. 27
5.2 NonparametricEstimatorsoftheComplexityFactor ............ 28
5.3 ParametricEstimationoftheComplexityFactor................ 30
5.4 TestingtheComplexityofaProcess.......................... 31
References ..................................................... 32
6 Principal Components Analysis of a Cyclostationary Random
Function .................................................. 35
AlainBoudouandSylvieViguier-Pla
6.1 Introduction.............................................. 35
6.2 PrerequisitesandNotation.................................. 36
6.3 PrincipalComponentsAnalysisintheFrequencyDomain ....... 37
6.4 RelationbetweentheSpaces𝐿2 (𝜉)and𝐿2 (A) ......... 38
𝐿2(A) 𝐿2(𝜉)
6.5 Cyclostationarity.......................................... 39
6.6 Definitionofa𝐿2(𝜉)−stationarySeriesfromaCyclostationaryr.f. 39
6.7 SimulationofaCyclostationaryr.f.andPCA.................. 40
References ..................................................... 42
7 LevelSetandDensityEstimationonManifolds .................. 43
AlejandroCholaquidis,RicardoFraimanandLeonardoMoreno
7.1 Introduction.............................................. 43
7.2 NotationandGeometricFramework.......................... 44
7.3 DensityEstimation ........................................ 45
7.4 LevelSetEstimation....................................... 46
7.5 ManifoldLevelSetEstimationunderr-convexity ............... 46
7.6 SimulationResults ........................................ 47
References ..................................................... 50
8 Pseudo-metricsasInterestingToolinNonparametricFunctional
Regression ................................................ 53
LaurentDelsolandAldoGoia
8.1 Introduction.............................................. 53
8.2 Pseudo-metricsuseinNon-parametricRegressiononFunctional
Variable ................................................. 54
8.3 OptimalPseudo-metricSelectioninPractice................... 56
8.4 SimulationStudies ........................................ 57
Contents ix
References ..................................................... 60
9 TestingaSpecificationForminSingleFunctionalIndexModel ..... 61
LaurentDelsolandAldoGoia
9.1 Introduction.............................................. 61
9.2 NotationandBasicPrinciple................................ 62
9.3 TheTestStatistic.......................................... 63
9.4 FiniteDimensionalPerformancesoftheTest .................. 64
9.5 Concludings.............................................. 66
References ..................................................... 67
10 ANewMethodforOrderingFunctionalDataanditsApplicationto
DiagnosticTest............................................. 69
GracielaEstévez-PérezandPhilippeVieu
10.1 Introduction.............................................. 69
10.2 SomeDiscussionaboutRanking:FromOnetoInfiniteDimensions 70
10.3 SomeDiscussionaboutROCCurvesandDiagnosticTest........ 70
10.4 AFlexibleFunctionalOrderingMethod ...................... 71
10.5 AFunctionalDiagnosticTest ............................... 73
References ..................................................... 74
11 AFunctionalDataAnalysisApproachtotheEstimationofDensities
overComplexRegions....................................... 77
FedericoFerraccioli,LauraM.Sangalli,EleonoraArnoneandLivio
Finos
11.1 Introduction.............................................. 77
11.2 Methodology............................................. 79
11.3 FutureResearch........................................... 80
References ..................................................... 81
12 A Conformal Approach for Distribution-free Prediction of
FunctionalData............................................ 83
Matteo Fontana, Simone Vantini, Massimo Tavoni and Alexander
Gammerman
12.1 Introduction.............................................. 84
12.2 ConformalPredictionforFunctionalVariables................. 84
12.3 FunctionalConformityMeasures ............................ 87
12.4 ApplicationtoIAMEnsembleForecasting .................... 87
References ..................................................... 88
13 G-LassoNetworkAnalysisforFunctionalData .................. 91
LaraFontanella,SaraFontanella,RosariaIgnaccolo,LuigiIppolitiand
PasqualeValentini
13.1 Introduction.............................................. 91
13.2 GraphicalModelsforFunctionalData ........................ 92
13.3 NetworkAnalysisontheCanadianWeather ................... 94
13.4 Discussion ............................................... 97