Abstract
Functional data analysis (FDA) is a fast growing area in statistical research with increasingly diverse range of application from economics, medicine, agriculture, chemometrics, etc. Functional regression is an area of FDA which has received the most
attention both in aspects of application and methodological development. Our main Functional data analysis (FDA) is a fast growing area in statistical research with increasingly diverse range of application from economics, medicine, agriculture, chemometrics,
etc. Functional regression is an area of FDA which has received the most attention both in aspects of application and methodological development. Our main concerns are two types of functional regression, namely, functional predictor regression
(scalar-on-function) and function-on-function regression. In particular, in the rst paper included in this thesis, we introduce multinomial functional regression model to analyze functional data with a categorical response (more than two classes)
and a functional predictor. To this end, a combination of discrete wavelet transform and LASSO penalization is considered. This model is applied to two datasets, one regarding lameness detection for horse and another regarding speech recognition.
In the second paper, we consider functional logistic regression via wavelet and LASSO which is a specic case of multinomial functional regression with two classes for the response and compare the eciency (from classication point of view) of
this model with two other models, namely, functional penalized regression and function regression using functional principle components. The comparison is based on simulation study and data application.
In the third paper, we study a constrained version of function-on-function regression, in which both response and predictor are dened at same domain and the prediction of the response at time t only depends on th concurrently observed predictor. We
introduce a version of this model for multilevel functional data of the type subjectunit, with the unit-level data being functional observations.
Finally, in the fourth paper we show how registration can be applied to functional data by considering a simple biomechanical constraint and the concerns are two types of functional regression, namely, functional predictor regression (scalar-on-function) and function-on-function regression. In particular, in the rst paper included in this thesis, we introduce multinomial functional regression model to analyze functional data with a categorical response (more than two classes) and a functional predictor. To this end, a combination of discrete wavelet transform and LASSO penalization is considered. This model is applied to two datasets, one
regarding lameness detection for horse and another regarding speech recognition.
In the second paper, we consider functional logistic regression via wavelet and LASSO which is a specic case of multinomial functional regression with two classes for the response and compare the eciency (from classication point of view) of
this model with two other models, namely, functional penalized regression and function regression using functional principle components. The comparison is based on simulation study and data application.
In the third paper, we study a constrained version of function-on-function regression, in which both response and predictor are dened at same domain and the prediction of the response at time t only depends on th concurrently observed predictor. We
introduce a version of this model for multilevel functional data of the type subjectunit, with the unit-level data being functional observations.
Finally, in the fourth paper we show how registration can be applied to functional data by considering a simple biomechanical constraint and then this approach is applied to a functional dataset from a juggling experiment.
attention both in aspects of application and methodological development. Our main Functional data analysis (FDA) is a fast growing area in statistical research with increasingly diverse range of application from economics, medicine, agriculture, chemometrics,
etc. Functional regression is an area of FDA which has received the most attention both in aspects of application and methodological development. Our main concerns are two types of functional regression, namely, functional predictor regression
(scalar-on-function) and function-on-function regression. In particular, in the rst paper included in this thesis, we introduce multinomial functional regression model to analyze functional data with a categorical response (more than two classes)
and a functional predictor. To this end, a combination of discrete wavelet transform and LASSO penalization is considered. This model is applied to two datasets, one regarding lameness detection for horse and another regarding speech recognition.
In the second paper, we consider functional logistic regression via wavelet and LASSO which is a specic case of multinomial functional regression with two classes for the response and compare the eciency (from classication point of view) of
this model with two other models, namely, functional penalized regression and function regression using functional principle components. The comparison is based on simulation study and data application.
In the third paper, we study a constrained version of function-on-function regression, in which both response and predictor are dened at same domain and the prediction of the response at time t only depends on th concurrently observed predictor. We
introduce a version of this model for multilevel functional data of the type subjectunit, with the unit-level data being functional observations.
Finally, in the fourth paper we show how registration can be applied to functional data by considering a simple biomechanical constraint and the concerns are two types of functional regression, namely, functional predictor regression (scalar-on-function) and function-on-function regression. In particular, in the rst paper included in this thesis, we introduce multinomial functional regression model to analyze functional data with a categorical response (more than two classes) and a functional predictor. To this end, a combination of discrete wavelet transform and LASSO penalization is considered. This model is applied to two datasets, one
regarding lameness detection for horse and another regarding speech recognition.
In the second paper, we consider functional logistic regression via wavelet and LASSO which is a specic case of multinomial functional regression with two classes for the response and compare the eciency (from classication point of view) of
this model with two other models, namely, functional penalized regression and function regression using functional principle components. The comparison is based on simulation study and data application.
In the third paper, we study a constrained version of function-on-function regression, in which both response and predictor are dened at same domain and the prediction of the response at time t only depends on th concurrently observed predictor. We
introduce a version of this model for multilevel functional data of the type subjectunit, with the unit-level data being functional observations.
Finally, in the fourth paper we show how registration can be applied to functional data by considering a simple biomechanical constraint and then this approach is applied to a functional dataset from a juggling experiment.
| Original language | English |
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| Publisher | Department of Mathematical Sciences, Faculty of Science, University of Copenhagen |
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| Number of pages | 129 |
| ISBN (Print) | 978-87-7078-940-0 |
| Publication status | Published - 2015 |