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:

  1. Are linear sieve estimators the same as Series estimators?
  2. Are splines just a specific serie estimator, when the basis is a specific one?
  3. Are there some sieve estimators that could not be written as a sum of weighted basis functions?

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