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

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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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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 907.

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Length: 25 pages
Date of creation: May 1989
Date of revision:
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: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

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

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References

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  1. Andrews, Donald W K, 1988. "Chi-Square Diagnostic Tests for Econometric Models: Theory," Econometrica, Econometric Society, vol. 56(6), pages 1419-53, November.
  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.
  3. 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.
  4. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
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Cited by:
  1. Hajivassiliou, 1993. "Macroeconomic Shocks in an Aggregative Disequilibrium Model," Cowles Foundation Discussion Papers 1063, Cowles Foundation for Research in Economics, Yale University.
  2. Sakata, Shinichi & White, Halbert, 2001. "S-estimation of nonlinear regression models with dependent and heterogeneous observations," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 5-72, July.
  3. Bruce E. Hansen, 1994. "Stochastic Equicontinuity for Unbounded Dependent Heterogeneous Arrays," Boston College Working Papers in Economics 295., Boston College Department of Economics.
  4. Arcones, Miguel A., 1996. "Weak convergence of stochastic processes indexed by smooth functions," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 115-138, March.
  5. 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 for Research in Economics, Yale University.
  6. Donald W.K. Andrews & David Pollard, 1990. "A Functional Central Limit Theorem for Strong Mixing Stochastic Processes," Cowles Foundation Discussion Papers 951, Cowles Foundation for Research in Economics, Yale University.

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