Uniform Convergence Of Series Estimators Over Function Spaces
This paper considers a series estimator of E [α( Y )|λ( X ) = λ̄], (α,λ) null 𝛢 × Λ, indexed by function spaces, and establishes the estimator's uniform convergence rate over λ̄ null R , α null 𝛢, and λ null Λ, when 𝛢 and Λ have a finite integral bracketing entropy. The rate of convergence depends on the bracketing entropies of 𝛢 and Λ in general. In particular, we demonstrate that when each λ null Λ is locally uniformly null 2 -continuous in a parameter from a space of polynomial discrimination and the basis function vector p null in the series estimator keeps the smallest eigenvalue of E [ p null (λ( X )) p null (λ( X ))‼] above zero uniformly over λ null Λ, we can obtain the same convergence rate as that established by de Jong (2002, Journal of Econometrics 111, 1–9).
Volume (Year): 24 (2008)
Issue (Month): 06 (December)
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