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Contributions to Statistics Teresa A. Oliveira · Christos P. Kitsos Amílcar Oliveira · Luís Grilo Editors Recent Studies on Risk Analysis and Statistical Modeling Contributions to Statistics The series Contributions to Statistics contains publications in theoretical and appliedstatistics, includingforexampleapplicationsin medicalstatistics, biomet- rics, econometrics and computational statistics. These publications are primarily monographsandmultipleauthorworkscontainingnewresearchresults,butconfer- enceandcongressreportsarealsoconsidered. Apartfromthecontributiontoscientificprogresspresented,itisanotablecharac- teristicoftheseriesthatpublishingtimeisveryshort,permittingauthorsandeditors topresenttheirresultswithoutdelay. Moreinformationaboutthisseriesathttp://www.springer.com/series/2912 Teresa A. Oliveira • Christos P. Kitsos • Amílcar Oliveira • Luís Grilo Editors Recent Studies on Risk Analysis and Statistical Modeling 123 Editors TeresaA.Oliveira ChristosP.Kitsos UniversidadeAberta DepartmentofInformatics Lisboa,Portugal TechnologicalEducationalInstituteof Athens Egaleo,Greece AmílcarOliveira LuísGrilo UniversidadeAberta UnidadeDeptdeMatematicaeFisica Lisboa,Portugal InstitutoPolitécnicodeTomar Tomar,Portugal ISSN1431-1968 ContributionstoStatistics ISBN978-3-319-76604-1 ISBN978-3-319-76605-8 (eBook) https://doi.org/10.1007/978-3-319-76605-8 LibraryofCongressControlNumber:2018943717 MathematicsSubjectClassification(2010):62-XX ©SpringerInternationalPublishingAG,partofSpringerNature2018 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Scientificprogressdependsongoodmethods,andinordertotrytoaccomplishthe developmentsinourdays,iturgestoexploreanddevelopmethodologiesinvolving risk analysis and statistical modeling.Trying to minimize or even avoid risks and to have good ways to be preparedto futureresults based on real data observedin thepastisinfactmandatory.Withrecentadvancesintheseareasfromtheoretical, computational, and practical points of view, the problems analysis has become morecomplex,andyetthereisa needforguidanceto getintothemoreadvanced literature.Mostofthisliteraturecanbefoundinscientificjournalsandproceedings. Besides some bookscover a few methodsverywell, most of them do notdo it in acomprehensiveway,mainlytothepractitionersintheseareas.Fromthispointof view,ourvolumedetachesthedifference.Thisbooktriestoovercomethatproblem by covering an essential part of the quantitative approach in risk analysis, where statisticalmodelsand/ormathematicalmethodsarelinkedwithsomephenomenon underinvestigation.Alongthebook,applicationstorealdataareobservedinseveral areas, like engineering, medicine, health sciences, education sciences, economy, finances,andindustry. Atthesametimemodelingissuesprovidethemethodologytogatheracompact structure for the data. In the first stage of risk analysis, data were studied from the decision theory point of view. However, nowadays data analysis is expanded to medical and biologicalmodels, and moreover,it coverseconomical, industrial, environmental, and management problems. Very general definition could be that: risk analysis is the review of (estimation of) the risks associated with a particular eventoraction,resultinginanotherone.Thatiswhyinprinciple,riskmanagement istheprocessofplanning,organizing,leading,andcontrollingactivitiestominimize the adverse effects of accidental losses on the organization, such as a firm or an industrial unit. Similar is the definition of the environmental risk assessment (ERA): it aims at assessing the effects of stressors, often chemicals, on the local environment. But risk assessment is concerned with the determination of quantitative or qualitative estimate of the associated risk related to a well-defined situationandarecognizedthreat:thus,thehazardfunctionisanessential“tool”for thethreatevaluation. v vi Preface The common target for risk assessment studies, either for toxicology/medicine or for biology/environmental,was the cancer risk assessment. Thus, interest was focused on the design of experiments and mixtures of experiments at the early stages,andlaterthestudyoftumorwasthroughthe“birth-death”stochasticprocess. Here the “risk” was the cell to be transformed to a tumor! The experiments of performing on rats were restricting from the “size of the experiment” for ethical and economic reasons. But such studies of risk cannot be applied on economic problems which need the estimation of the involved risk. Actuary mathematics is anotherapproachtoreducetheriskforinsurancecompaniesandothers. OurpreviousSpringervolumeinTheoryandPracticeofRiskAssessmentreflects a first step to extend the applications of risk analysis, to obtain a broader area of research, rather than the one centered on biostatistics, as an extension (political) fromgametheory. Needless to say, at the first stage of using risk methods, from a mathematical point of view relative risk was really a simple index, but so useful (distance) measure. We adopt this line of thought in this volume, thanks to Springer, and we include more areas of applying risk theory. Thus, we believe that we cement our point of view that risk analysis can be considered an independent branch of statistics,tacklingareasofinterestsuchasmanagement,industry,andeconomics. The problem of data is always at the first line of interest, not only if it exists or not. We must recall that in cases where the data set is small, less than 30 observations,orforbigdatasets,weneedaspecialtreatmentofthedata.Insome cases(duetocost!)onlyveryfewobservationscanbeobtained.Wemovedfromthe “dataofstatus”thatisstatisticstoanalyzingdatasetsfromanumberofareas,when weweredevelopingDataAnalysis(thankstoJohnTukey,whonamedthemethod) and,nowdealingwithbigdatasetsandhigh-techcomputers,wearemovingtoData Analytics(subsetofBusinessIntelligence).Butalwaysthesourceofdatawetryto analyze is very essential and related to the risk we try to eliminate, minimize, or estimate. It was essential to create biological data sets. Molecular biology through genomics, proteomics, and metabolomics increased our knowledge of biological processes, and several databases are now accessible through the Internet. Similar databases,notsoeasyaccessible,weredevelopedoncancer.Studiesonriskanalysis were therefore based on more reliable data sets, as far as cancer was concerned. Statisticalmodelingalsotacklesthedataanalysisproblem.Thatiswhythisbookis dividedintotwoparts: PartI.RiskMethodologiesandApplications PartII.StatisticalModelingandRiskIssuesinSeveralAreas The papers submitted to this volume were carefully reviewed by referees. The selected paperswere placed appropriatelyand offerthe readersthe opportunityto lookforanumberofdifferentapproachesandabroadrangeofareasofapplication. Webelievethatthisbookwilloffersolutionstotheexistingproblems,willprovide the appropriateframeworkand backgroundto real-life problems,and will covera Preface vii gapthatusuallyexists:somemoretimeisneededfornewtheoreticalresultstobe publishedinonebook. The book reflects contributionsfrom invited experts, providingthe reader with acomprehensiveoverviewofthemainareasbyfosteringlinkswithseveralrelated disciplines, exploring computational issues, and presenting some research future trends. As this volume is multiauthor, multinational and covers different areas of applications,itoffersachancetotheresearchersworkingindifferentareasofhaving itasareferencebook. Lisboa,Portugal TeresaA.Oliveira Athens,Greece ChristosP.Kitsos Lisboa,Portugal AmílcarOliveira Tomar,Portugal LuísGrilo Introduction Doubtisthebeginning,nottheend,ofwisdom. —GeorgeIles,1852–1942. Infact,doubtraisesthenotionofhazard,promotesriskresearchandfostersnew knowledge.This book tries to coveran essential part of the quantitativeapproach inRiskAnalysis,wherestatisticalmodelsand/ormathematicalmethodsarelinked withsomephenomenonunderinvestigation.ThegeneraltopicRISKisexploredin order to understand, simulate, design and promote the analysis of real problems, fostering new challenges in several areas, such as Engineering, Medicine, Health Sciences,EducationSciences,Economy,FinancesandIndustry. In an attempt to recognize the role that statistics and computation play in risk analysis, the International Committee on Risk Analysis of the International StatisticalInstitute,theISI-CRA,decidedtoselectaseriesofinterestingpapersin ordertoattemptasthisbookchapters,consistingofsomeofthemostimportantand current methodologies under the Risk topic. With this book we aim to reinforce the bridge connecting theoretical topics and new methodologies to the practical applications,fosteringadeepinsightamongthepractitionersofseveralareas. Thebookispresentedintotwomainpartsbasedonthesubjectmattercovered: PartIisdevotedtoRiskMethodologiesandApplications PartIIisfocusedonStatisticalModelingandRiskIssuesinSeveralAreas Part I:RiskMethodologies andApplications The papers in Part I mainly cover Risk theoretical issues and methodologies, with focus on applications in Health Sciences, Medicine, Economics, Finance, EngineeringandonspecialissuesinthemainareasofMathematicsandStatistics. ix x Introduction Thechaptersare organizedinto sectionsbasedon the primaryfocusof the papers included.Somebrieflydescriptionofthetopicscoveredinthesesectionsfollows: Section 1 The first section deals with Risk Analysis in Health Sciences and Medicine. Chapter“AssessmentofMaximumAPosterioriImageEstimationAlgorithmsfor ReducedAcquisitionTimeMedicalPositronEmissionTomographyData”considers a study to examine the effects of reduced radioactive dosage data collection on positronemissionstomographyreconstructionreliability.Theefficiencyofvarious reconstructionmethodsisalsoinvestigated. Chapter “On Mixed Cancer Risk Assessment” consider both mammary cancer and Wilms tumors, as two typical examples from oncology generating difficult multicriterial decision problems. The authors fit mixture models to box-counting fractal dimensions in order to better understand the variability, they explore the effect of chemotherapyand present a discussion on the shape analysis for Wilms tumors. Section 2 The second section is devoted to Risk Analysis in Economics and Financeapplications. Chapter “Traditional Versus Alternative Risk Measures in Hedge Fund Invest- mentEfficiency”dealswiththeHedgefundswhicharefinancialinstitutionsaiming at generating absolute rates of return, that is at realizing profits regardless of the market situation. Some measures of investment are explored and compared in a particularperiod. Chapter “Estimating the Extremal Coefficient: A Simulation Comparison of Methods”.Taildependenceisanimportantissuetoevaluateriskandthemultivari- ateextremevaluestheoryisthemostsuitabletodealwiththeextremaldependence. Theextremalcoefficientmeasuresthedegreeofdependencebetweenthemarginals ofmax-stabledistributions,anaturalclassofmodelsinthisframework.Theauthors addresstheestimationoftheextremalcoefficientandanewestimatoriscompared through simulation with existing methods. An illustration with real data is also presented. InChapter“OnaBusinessConfidenceIndexandItsDataAnalytics:AChilean Case” a methodologyon a novelChilean business confidence index is presented, which allows the description of some aspects of the market at a global level, as wellasatindustrialandsectorlevelsofChileangreatbrands.Someissuesrelated tobusinessintelligence,customerandbusinesssurveys,marketvariablesandofthe mentionedconfidenceindexarediscussed.DescriptiveandInferentialresultsonthis indexarepresented,aswell asresults onthe competitivenessof the Chilean great brands. InChapter“OntheApplicationofSampleCoefficientofVariationforManaging Loan Portfolio Risks” the application of Sample Coefficient of Variation for ManagingLoanPortfolioRiskispresented.Theauthorsobtainthelowerandupper bounds for sample Coefficient Variation and study the possibility of using it for measuring the risk concentration in a loan portfolio. The capital adequacy and thesingleborrowerlimitareconsideredandsometheoreticalresultsareobtained.