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An Empirical Process Central Limit Theorem for Dependent Non-Identically Distributed Random Variables

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Author Info
Donald W.K. Andrews () (Cowles Foundation, Yale University)

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Abstract

This paper establishes a central limit theorem (CLT) for empirical processes indexed by smooth functions. The underlying random variables may be temporally dependent and non-identically distributed. In particular, the CLT holds for near epoch dependent (i.e., functions of mixing processes) triangular arrays, which include strong mixing arrays, among others. The results apply to classes of functions that have series expansions. The proof of the CLT is particularly simple; no chaining argument is required. The results can be used to establish the asymptotic normality of semiparametric estimators in time series contexts. An example is provided.

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File URL: http://cowles.econ.yale.edu/P/cd/d09a/d0907.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 907.

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Length: 25 pages
Date of creation: May 1989
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Publication status: Published in Journal of Multivariate Analysis (August 1991), 38(2): 188-203
Handle: RePEc:cwl:cwldpp:907

Note: CFP 792.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Central limit theorem; empirical process; Fourier series; semiparametric estimator; time series;

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References listed on IDEAS
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. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-91, July. [Downloadable!] (restricted)
  2. Andrews, Donald W. K., 1988. "Chi-square diagnostic tests for econometric models : Introduction and applications," Journal of Econometrics, Elsevier, vol. 37(1), pages 135-156, January. [Downloadable!] (restricted)
  3. Andrews, Donald W K, 1988. "Chi-Square Diagnostic Tests for Econometric Models: Theory," Econometrica, Econometric Society, vol. 56(6), pages 1419-53, November. [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. Hajivassiliou, 1993. "Macroeconomic Shocks in an Aggregative Disequilibrium Model," Cowles Foundation Discussion Papers 1063, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  2. Bruce E. Hansen, 1994. "Stochastic Equicontinuity for Unbounded Dependent Heterogeneous Arrays," Boston College Working Papers in Economics 295., Boston College Department of Economics. [Downloadable!]
    Other versions:
  3. Donald W.K. Andrews, 1992. "An Introduction to Econometric Applications of Functional Limit Theory for Dependent Random Variables," Cowles Foundation Discussion Papers 1020, Cowles Foundation, Yale University. [Downloadable!]
  4. Donald W.K. Andrews & David Pollard, 1990. "A Functional Central Limit Theorem for Strong Mixing Stochastic Processes," Cowles Foundation Discussion Papers 951, Cowles Foundation, Yale University. [Downloadable!]
  5. Halbert White & Yongmiao Hong, 1999. "M-Testing Using Finite and Infinite Dimensional Parameter Estimators," University of California at San Diego, Economics Working Paper Series 93-01r, Department of Economics, UC San Diego. [Downloadable!]
    Other versions:
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