Representing functional data as smooth functions
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The basic philosophy of functional data analysis is that we should think of observed data functions as single entities, rather than merely a sequence of individual observations. The term functional refers to the intrinsic structure of the data rather than to their explicit form. But in practice, functional data are usually observed and recorded discretely. A record of a functional observation x consists of n pairs (t j ,y j ), where y j is a recording or observation of x(t j ), a snapshot of the function at argument value t j .
KeywordsDiscrete Wavelet Transform Functional Data Observational Error Kernel Smoothing Polynomial Spline
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