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An investigation into Functional Linear Regression Modeling
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 applicati...
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| Format: | Thesis |
| Language: | English |
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Department of Statistical Sciences
2015
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| _version_ | 1867613222236848128 |
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| access_status_str | Open Access |
| author | Essomba, Rene Franck |
| author2 | Lubbe, Sugnet |
| author_browse | Essomba, Rene Franck Lubbe, Sugnet |
| author_facet | Lubbe, Sugnet Essomba, Rene Franck |
| author_sort | Essomba, Rene Franck |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/15591 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:42.829Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| publisher | Department of Statistical Sciences |
| publisherStr | Department of Statistical Sciences |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/15591 An investigation into Functional Linear Regression Modeling Essomba, Rene Franck Lubbe, Sugnet Mathematical Statistics Functional Data Analysis Basis Expansion Functional Regression Smoothing Techniques 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. 2015-12-04T18:05:19Z 2015-12-04T18:05:19Z 2015 Master Thesis Masters MSc http://hdl.handle.net/11427/15591 eng application/pdf Department of Statistical Sciences Faculty of Science University of Cape Town |
| spellingShingle | Mathematical Statistics Functional Data Analysis Basis Expansion Functional Regression Smoothing Techniques Essomba, Rene Franck An investigation into Functional Linear Regression Modeling |
| thesis_degree_str | Master's |
| title | An investigation into Functional Linear Regression Modeling |
| title_full | An investigation into Functional Linear Regression Modeling |
| title_fullStr | An investigation into Functional Linear Regression Modeling |
| title_full_unstemmed | An investigation into Functional Linear Regression Modeling |
| title_short | An investigation into Functional Linear Regression Modeling |
| title_sort | investigation into functional linear regression modeling |
| topic | Mathematical Statistics Functional Data Analysis Basis Expansion Functional Regression Smoothing Techniques |
| url | http://hdl.handle.net/11427/15591 |
| work_keys_str_mv | AT essombarenefranck aninvestigationintofunctionallinearregressionmodeling AT essombarenefranck investigationintofunctionallinearregressionmodeling |