As far as I know, Sieve Estimators consists in a broader class of estimators for a function g(x) lying in a space of functions G. The estimation basically consists in choosing the function that best approximates g(x) in a subspace Gn of G. This subspace Gn would grow as n grows.
I know also that Series estimators are a subclass of sieve estimators that could be written as a weighted sum of basis functions.
Here comes my questions:
- Are linear sieve estimators the same as Series estimators?
- Are splines just a specific serie estimator, when the basis is a specific one?
- Are there some sieve estimators that could not be written as a sum of weighted basis functions?