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Lecturer(s)
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Hron Karel, prof. RNDr. Ph.D., DSc.
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Machalová Jitka, doc. RNDr. Ph.D., MBA
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Course content
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1. Basis representation of splines in R^1 2. B-splines and their fundamental properties 3. Interpolation and the least squares method using splines 4. Penalized least squares method using splines 5. Tensor product splines 6. Data approximation using tensor product splines 7. Exploratory functional data analysis and FPCA (functional principal component analysis) 8. Mathematical foundations of functional data analysis 9. Regression with a functional predictor variable 10. Regression with a functional response variable 11. Sparse functional data analysis 12. Functional time series 13. Spatial functional data
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming), Demonstration
- Preparation for the Course Credit
- 20 hours per semester
- Attendace
- 52 hours per semester
- Preparation for the Exam
- 40 hours per semester
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Learning outcomes
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The objective of this course is to understand the methods used for the approximation and analysis of functional data, including their implementation in statistical software.
Application Apply numerical methods, probability theory and mathematical statistics to approximation and methods of functional data analysis.
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Prerequisites
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Basic knowledge of numerical methods, probability theory, and multivariate statistics.
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Assessment methods and criteria
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Oral exam, Seminar Work
Zápočet: praktická implementace aproximačních technik, prezentace projektu pokrývajícího témata analýzy funkcionálních dat Zkouška: ústní zkouška
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Recommended literature
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Crainiceanu, C., Goldsmith, J., Leroux, A., Cui, E. (2024). Functional data analysis with R. Boca Raton.
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de Boor, C. (1978). A Practical Guide to Splines. New York.
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Dierckx P. (1993). Curve and Surface Fitting with Splines.
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Kokoszka, P., Reimherr, M. (2017). Introduction to functional data analysis. CRC Press.
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Ramsay, J.O., Hooker, G., Graves, S. (2009). Functional data analysis with R and MATLAB. New York.
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Ramsay, J.O., Silverman, B.W. (2005). Functional data analysis. New York.
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Schumaker, L. L. (2007). Spline functions: basic theory. Cambridge.
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