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Functional data are defined by curves or images. The goals of functional data analysis (FDA) are those of statistics in general: To study variation and to propose models. Because the processes that generate functional data are usually smooth, we can use derivatives to impose smoothness on estimated functions, and we can construct differential equations to model the functional data.
We will first review basic techniques for manipulating functional data including smoothing methods. The registration problem, involving aligning salient features across several curves, will be a central issue. We then consider functional versions of analysis of variance, regression and principal components. Differential equations, being also functional linear models, can also be estimated from functional data.
The workshop will be based on the books, Functional Data Analysis (1997) and Applied Functional Data Analysis (2002) by J. O. Ramsay and B. W. Silverman and published by Springer, and on a revision of the first book that is in progress. Copies of these books will be available for sale. The workshop will also use software developed for both S-PLUS and Matlab, and sample data and analyses will be available.
Fifteen reimbursements up to $200.00 for expenses are available to students coming from out of town.
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