Sieves

In this chapter, we study nonparametric regression estimators based on sieves. Here, a sieve is taken to be a nested sequence of finite-dimensional subspaces of the ambient L ² space. This is somewhat different from the alternative interpretation of a sieve as a nested sequence of compact subsets of the L ² space; see § 12.2. Either way, a sieved estimator is defined as the solution to a minimization problem, e.g., least-squares or maximum likelihood, with the solution constrained to be a member of the sieve.