Q: For which data is it appropriate to use state-space modeling and Kalman filtering instead of smoothing splines and vice versa? Is there some equivalence relationship between the two?
I'm trying to get some high-level understanding of how these methods fit together. I browsed through Johnstone's new Gaussian Estimation: Sequence and Multiresolution Models. It surprised be that there was not one mention of state-space models and Kalman filtering. Why wouldn't that be in there? Isn't that the most standard tool for these sort of problems? The focus, instead, was on smoothing splines and wavelet thresholding. I'm now very confused.