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Uniform Convergence Of Series Estimators Over Function Spaces

  • Song, Kyungchul
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    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)) pnull (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).

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    Article provided by Cambridge University Press in its journal Econometric Theory.

    Volume (Year): 24 (2008)
    Issue (Month): 06 (December)
    Pages: 1463-1499

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    Handle: RePEc:cup:etheor:v:24:y:2008:i:06:p:1463-1499_08
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