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On the Formulation of Uniform Laws of Large Numbers: A Truncation Approach

  • Benedikt M. Potscher
  • Ingmar R. Prucha

The paper develops a general framework for the formulation of generic uniform laws of large numbers. In particular, we introduce a basic generic uniform law of large numbers that contains recent uniform laws of large numbers by Andrews [2] and Hoadley [7J as special cases. We also develop a truncation approach .that makes it possible to obtain uniform laws of large numbers for the functions under consideration from uniform laws of large numbers for truncated versions of those functions. The point of the truncation approach is that uniform laws of large numbers for the truncated versions are typically easier to obtain. By combining the basic uniform law of large numbers and the truncation approach we also derive generalizations of recent uniform laws of large numbers introduced in Potscher and Prucha [13, l5].

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File URL: http://www.nber.org/papers/t0085.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0085.

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Date of creation: Apr 1994
Date of revision:
Publication status: published as Statistics, vo. 25, (1994), pp. 343-360
Handle: RePEc:nbr:nberte:0085
Note: PR
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  1. White, Halbert, 1980. "Nonlinear Regression on Cross-Section Data," Econometrica, Econometric Society, vol. 48(3), pages 721-46, April.
  2. Domowitz, Ian & White, Halbert, 1982. "Misspecified models with dependent observations," Journal of Econometrics, Elsevier, vol. 20(1), pages 35-58, October.
  3. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-61, January.
  4. Potscher, Benedikt M. & Prucha, Ingmar R., 1987. "A Uniform Law of Large Numbers for Dependent and Heterogeneous Data Process," Working Papers 87-26, C.V. Starr Center for Applied Economics, New York University.
  5. Bates, Charles & White, Halbert, 1985. "A Unified Theory of Consistent Estimation for Parametric Models," Econometric Theory, Cambridge University Press, vol. 1(02), pages 151-178, August.
  6. Donald W.K. Andrews, 1986. "Consistency in Nonlinear Econometric Models: A Generic Uniform Law of Large Numbers," Cowles Foundation Discussion Papers 790, Cowles Foundation for Research in Economics, Yale University.
  7. David Levine, 1981. "A Remark on Serial Correlation in Maximum Likelihood," UCLA Economics Working Papers 215, UCLA Department of Economics.
  8. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
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