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An empirical process central limit theorem for dependent non-identically distributed random variables

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  • Andrews, Donald W. K.

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 38 (1991)
Issue (Month): 2 (August)
Pages: 187-203

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Handle: RePEc:eee:jmvana:v:38:y:1991:i:2:p:187-203

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Related research

Keywords: central limit theorem empirical process Fourier series functional central limit theorem near epoch dependence semiparametric estimator series expansion Sobolev norm stochastic equicontinuity strong mixing;

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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. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
  4. 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.
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Cited by:
  1. Bruce E. Hansen, 1994. "Stochastic Equicontinuity for Unbounded Dependent Heterogeneous Arrays," Boston College Working Papers in Economics 295., Boston College Department of Economics.
  2. Hajivassiliou, 1993. "Macroeconomic Shocks in an Aggregative Disequilibrium Model," Cowles Foundation Discussion Papers 1063, Cowles Foundation for Research in Economics, Yale University.
  3. 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.
  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 for Research in Economics, Yale University.
  5. 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.
  6. 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.

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