An investigation into Functional Linear Regression Modeling

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dc.contributor.advisorLubbe, Sugneten_ZA
dc.contributor.authorEssomba, Rene Francken_ZA
dc.date.accessioned2015-12-04T18:05:19Z
dc.date.available2015-12-04T18:05:19Z
dc.date.issued2015en_ZA
dc.description.abstractFunctional data analysis, commonly known as FDA", refers to the analysis of information on curves of functions. Key aspects of FDA include the choice of smoothing techniques, data reduction, model evaluation, functional linear modeling and forecasting methods. FDA is applicable in numerous applications such as Bioscience, Geology, Psychology, Sports Science, Econometrics, Meteorology, etc. This dissertation main objective is to focus more specifically on Functional Linear Regression Modelling (FLRM), which is an extension of Multivariate Linear Regression Modeling. The problem of constructing a Functional Linear Regression modelling with functional predictors and functional response variable is considered in great details. Discretely observed data for each variable involved in the modelling are expressed as smooth functions using: Fourier Basis, B-Splines Basis and Gaussian Basis. The Functional Linear Regression Model is estimated by the Least Square method, Maximum Likelihood method and more thoroughly by Penalized Maximum Likelihood method. A central issue when modelling Functional Regression models is the choice of a suitable model criterion as well as the number of basis functions and an appropriate smoothing parameter. Four different types of model criteria are reviewed: the Generalized Cross-Validation, the Generalized Information Criterion, the modified Akaike Information Criterion and Generalized Bayesian Information Criterion. Each of these aforementioned methods are applied to a dataset and contrasted based on their respective results.en_ZA
dc.identifier.apacitationEssomba, R. F. (2015). <i>An investigation into Functional Linear Regression Modeling</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Statistical Sciences. Retrieved from http://hdl.handle.net/11427/15591en_ZA
dc.identifier.chicagocitationEssomba, Rene Franck. <i>"An investigation into Functional Linear Regression Modeling."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Statistical Sciences, 2015. http://hdl.handle.net/11427/15591en_ZA
dc.identifier.citationEssomba, R. 2015. An investigation into Functional Linear Regression Modeling. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Essomba, Rene Franck AB - Functional data analysis, commonly known as FDA", refers to the analysis of information on curves of functions. Key aspects of FDA include the choice of smoothing techniques, data reduction, model evaluation, functional linear modeling and forecasting methods. FDA is applicable in numerous applications such as Bioscience, Geology, Psychology, Sports Science, Econometrics, Meteorology, etc. This dissertation main objective is to focus more specifically on Functional Linear Regression Modelling (FLRM), which is an extension of Multivariate Linear Regression Modeling. The problem of constructing a Functional Linear Regression modelling with functional predictors and functional response variable is considered in great details. Discretely observed data for each variable involved in the modelling are expressed as smooth functions using: Fourier Basis, B-Splines Basis and Gaussian Basis. The Functional Linear Regression Model is estimated by the Least Square method, Maximum Likelihood method and more thoroughly by Penalized Maximum Likelihood method. A central issue when modelling Functional Regression models is the choice of a suitable model criterion as well as the number of basis functions and an appropriate smoothing parameter. Four different types of model criteria are reviewed: the Generalized Cross-Validation, the Generalized Information Criterion, the modified Akaike Information Criterion and Generalized Bayesian Information Criterion. Each of these aforementioned methods are applied to a dataset and contrasted based on their respective results. DA - 2015 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2015 T1 - An investigation into Functional Linear Regression Modeling TI - An investigation into Functional Linear Regression Modeling UR - http://hdl.handle.net/11427/15591 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/15591
dc.identifier.vancouvercitationEssomba RF. An investigation into Functional Linear Regression Modeling. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Statistical Sciences, 2015 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/15591en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Statistical Sciencesen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematical Statisticsen_ZA
dc.subject.otherFunctional Data Analysisen_ZA
dc.subject.otherBasis Expansionen_ZA
dc.subject.otherFunctional Regressionen_ZA
dc.subject.otherSmoothing Techniquesen_ZA
dc.titleAn investigation into Functional Linear Regression Modelingen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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