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

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Benedikt M. Potscher
Ingmar R. Prucha

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Abstract

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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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
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Handle: RePEc:nbr:nberte:0085

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  1. Levine, David, 1983. "A remark on serial correlation in maximum likelihood," Journal of Econometrics, Elsevier, vol. 23(3), pages 337-342, December. [Downloadable!] (restricted)
  2. Potscher, Benedikt M & Prucha, Ingmar R, 1989. "A Uniform Law of Large Numbers for Dependent and Heterogeneous Data Processes," Econometrica, Econometric Society, vol. 57(3), pages 675-83, May. [Downloadable!] (restricted)
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  3. David K. Levine, 1983. "A Remark on Serial Correlation in Maximum Likelihood," Levine's Working Paper Archive 176, David K. Levine. [Downloadable!]
  4. White, Halbert, 1980. "Nonlinear Regression on Cross-Section Data," Econometrica, Econometric Society, vol. 48(3), pages 721-46, April. [Downloadable!] (restricted)
  5. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  6. Domowitz, Ian & White, Halbert, 1982. "Misspecified models with dependent observations," Journal of Econometrics, Elsevier, vol. 20(1), pages 35-58, October. [Downloadable!] (restricted)
  7. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-61, January. [Downloadable!] (restricted)
  8. Charles Bates & Halbert White, 1984. "A Unified Theory of Consistent Estimation for Parametric Models," Working papers 359, Massachusetts Institute of Technology (MIT), Department of Economics.
  9. Donald W.K. Andrews, 1986. "Consistency in Nonlinear Econometric Models: A Generic Uniform Law of Large Numbers," Cowles Foundation Discussion Papers 790, Cowles Foundation, Yale University. [Downloadable!]
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