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Generic Uniform Convergence

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

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Abstract

This paper presents several generic uniform convergence results that include generic uniform laws of large numbers. These results provide conditions under which pointwise convergence almost surely or in probability can be strengthened to uniform convergence. The results are useful for establishing asymptotic properties of estimators and test statistics. The results given here have the following attributes, (1) they extend results of Newey to cover convergence almost surely as well as convergence in probability, (2) they apply to totally bounded parameter spaces (rather than just to compact parameter spaces), (3) they introduce a set of conditions for a generic uniform law of large numbers that has the attribute of giving the weakest conditions available for iid contexts, but which apply in dependent non-identically distributed contexts as well, and (4) they incorporate and extend the main results in the literature in a parsimonious fashion.

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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 940.

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Length: 21 pages
Date of creation: Mar 1990
Date of revision:
Publication status: Published in Econometric Theory (1992), 8: 241-257
Handle: RePEc:cwl:cwldpp:940

Note: CFP 810.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
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: Consistency; law of large numbers; uniform convergence; asymptotic theory; test statistics; estimators;

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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. Filippo Altissimo & Valentina Corradi, 2000. "Strong Rules for Detecting the Number of Breaks in a Time Series," Econometric Society World Congress 2000 Contributed Papers 0574, Econometric Society. [Downloadable!]
    Other versions:
  2. Donald W.K. Andrews & Biao Lu, 1999. "Consistent Model and Moment Selection Criteria for GMM Estimation with Applications to Dynamic Panel Data Models," Cowles Foundation Discussion Papers 1233, Cowles Foundation, Yale University. [Downloadable!]
  3. Eric Ghysels & Alain Guay, 2001. "Testing for Structural Change in the Presence of Auxiliary Models," Cahiers de recherche CREFE / CREFE Working Papers 133, CREFE, Université du Québec à Montréal. [Downloadable!]
    Other versions:
  4. Cizek, P., 2007. "General Trimmed Estimation: Robust Approach to Nonlinear and Limited Dependent Variable Models (Replaced by DP 2007-65)," Discussion Paper 2007-1, Tilburg University, Center for Economic Research.
  5. Valentina Corradi & Norman R. Swanson, 2003. "Bootstrap Conditional Distribution Tests In the Presence of Dynamic Misspecification," Departmental Working Papers 200311, Rutgers University, Department of Economics. [Downloadable!]
    Other versions:
  6. Donald W.K. Andrews & Werner Ploberger, 1993. "Admissibility of the Likelihood Ratio Test When a Nuisance Parameter Is Present OnlyUnder the Alternative," Cowles Foundation Discussion Papers 1058, Cowles Foundation, Yale University. [Downloadable!]
  7. Eric Ghysels & Alain Guay, 1998. "Structural Change Tests for Simulated Method of Moments," CIRANO Working Papers 98s-19, CIRANO. [Downloadable!]
    Other versions:
  8. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2005. "Bias Corrected Instrumental Variables Estimation for Dynamic Panel Models with Fixed E¤ects," Boston University - Department of Economics - Working Papers Series WP2005-024, Boston University - Department of Economics. [Downloadable!]
  9. Donald W.K. Andrews & Werner Ploberger, 1994. "Testing for Serial Correlation Against an ARMA(1,1) Process," Cowles Foundation Discussion Papers 1077, Cowles Foundation, Yale University. [Downloadable!]
  10. Donald W.K. Andrews & C. John McDermott, 1993. "Nonlinear Econometric Models with Deterministically Trending Variables," Cowles Foundation Discussion Papers 1053, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  11. Ramdan Dridi, 2000. "Simulated Asymptotic Least Squares Theory," STICERD - Econometrics Paper Series /2000/396, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  12. M. Hashem Pesaran & Yongcheol Shin, 2002. "Long-Run Structural Modelling," Econometric Reviews, Taylor and Francis Journals, vol. 21(1), pages 49-87. [Downloadable!] (restricted)
    Other versions:
  13. Cizek, P., 2004. "General trimmed estimation: robust approach to nonlinear and limited dependent variable models," Discussion Paper 130, Tilburg University, Center for Economic Research. [Downloadable!]
  14. 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!]
  15. Joris Pinkse, 2000. "Feasible Multivariate Nonparametric Estimation Using Weak Separability," Econometric Society World Congress 2000 Contributed Papers 1241, Econometric Society. [Downloadable!]
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