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Terrible Functional Data Analysis?

Today I read a Chinese paper about the “Function Data Analysis” and I was greatly surprised at what he described in the paper. Currently I’m not familiar with functional data at all, but he told us such a kind of “data” was just the result of applying a (some) smoothing function(s) to the original discrete observations, so the sample points became continuous (actually they became functions). These smoothing functions might either be Fourier transformations or B-splines.

I wonder whether there are some rules about the choice of smoothing functions, because if there aren’t any, the functional data will be rather free, and I cannot believe such a kind of data can really represent information behind these discrete data points: who knows what happens between two observations?! Only my naive ideas… -_-//