{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/15591"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/15591","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"An investigation into Functional Linear Regression Modeling","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Essomba, Rene Franck"],"institution":"Department of Statistical Sciences","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Lubbe, Sugnet"],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015","date_published":"2015","updated_at":"2026-07-22T22:22:58Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/15591","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Lubbe, Sugnet"]},{"key":"dc:creator","label":"Author","values":["Essomba, Rene Franck"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2015-12-04T18:05:19Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2015-12-04T18:05:19Z"]},{"key":"dc:date.issued","label":"Date","values":["2015"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Statistical Sciences"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/15591"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["An investigation into Functional Linear Regression Modeling"]}]}],"canonical_facts":{"dc:contributor.advisor":["Lubbe, Sugnet"],"dc:creator":["Essomba, Rene Franck"],"dc:date.accessioned":["2015-12-04T18:05:19Z"],"dc:date.available":["2015-12-04T18:05:19Z"],"dc:date.issued":["2015"],"dc:description.abstract":["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."],"dc:identifier.uri":["http://hdl.handle.net/11427/15591"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Statistical Sciences"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["An investigation into Functional Linear Regression Modeling"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:22:58Z"}