I have a data set that I wish to analyze using functional data analysis methods. Data consists of repeated measures of some characteristic on a number of inviduals. I have the time of the measurements and these differ between individuals. So far, I see no problem in analyzing this, e.g. by using ready-to-use ${\tt R}$ packages. However, the number of measurements per individual differs as well for my data. How can I handle this? Can anyone point me in the direction of literature on this set-up or any packages that can handle it?
What I want to do with data to start with is basically something like functional linear model (functional response and scalar predictors).
I'm aware that I could smooth the data using a very light smoothing procedure (using many basis functions and no or a very small penalty parameter) and use these smoothed curves for my analysis. But is this the best way to approach the problem? It doesn't take into account that some curves are determined with more precision than are others. An additional problem to this approach is that some of the individuals only have measurements in a subinterval (say, [200, 1000]) of the full interval of the majority of the curves (say, [0, 1000]). Thus, the smooth would be very poorly estimated in those regions. Naturally, I could restrict attention to the interval [200, 1000] but this seems like a waste of data.
To sum up my question, what would you do in this case? Any thoughts and hints will be much appreciated.