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Central Limit And Functional Central Limit Theorems For Hilbert-Valued Dependent Heterogeneous Arrays With Applications

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Author Info
Chen, Xiaohong
White, Halbert

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Abstract

We obtain new central limit theorems (CLT s) and functional central limit theorems (FCLT s) for Hilbert-valued arrays near epoch dependent on mixing processes, and also new FCLT s for general Hilbert-valued adapted dependent heterogeneous arrays. These theorems are useful in delivering asymptotic distributions for parametric and nonparametric estimators and their functionals in time series econometrics. We give three significant applications for near epoch dependent observations: (1) A new CLT for any plug-in estimator of a cumulative distribution function (c.d.f.) (e.g., an empirical c.d.f., or a c.d.f. estimator based on a kernel density estimator), which can in turn deliver distribution results for many Von Mises functionals; (2) a new limiting distribution result for degenerate U-statistics, which delivers distribution results for Bierens s integrated conditional moment tests; (3) a new functional central limit result for Hilbert-valued stochastic approximation procedures, which delivers distribution results for nonparametric recursive generalized method of moment estimators, including nonparametric adaptive learning models.

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

Volume (Year): 14 (1998)
Issue (Month): 02 (April)
Pages: 260-284
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Handle: RePEc:cup:etheor:v:14:y:1998:i:02:p:260-284_14

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Bierens, H. & Ploberger, W., 1995. "Asymptotic theory of integrated conditional moment tests," Discussion Paper 124, Tilburg University, Center for Economic Research. [Downloadable!]
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  2. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. J. Carlos Escanciano & Carlos Velasco, 2003. "Generalized Spectral Tests For The Martingale Difference Hypothesis," Statistics and Econometrics Working Papers ws035212, Universidad Carlos III, Departamento de Estadística y Econometría. [Downloadable!]
    Other versions:
  2. Jonathan B. Hill, 2005. "On Tail Index Estimation Using Dependent,Heterogenous Data," Working Papers 0512, Florida International University, Department of Economics. [Downloadable!]
  3. Jonathan B. Hill, 2005. "On Tail Index Estimation for Dependent, Heterogenous Data," Econometrics 0505005, EconWPA, revised 27 May 2005. [Downloadable!]
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