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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

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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Bibliographic Info

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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Publication status: published as Statistics, vo. 25, (1994), pp. 343-360
Handle: RePEc:nbr:nberte:0085

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  1. Charles Bates & Halbert White, 1984. "A Unified Theory of Consistent Estimation for Parametric Models," Working papers, Massachusetts Institute of Technology (MIT), Department of Economics 359, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. Donald W.K. Andrews, 1986. "Consistency in Nonlinear Econometric Models: A Generic Uniform Law of Large Numbers," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 790, Cowles Foundation for Research in Economics, Yale University.
  3. David K. Levine, 1983. "A Remark on Serial Correlation in Maximum Likelihood," Levine's Working Paper Archive 176, David K. Levine.
  4. Potscher, Benedikt M & Prucha, Ingmar R, 1989. "A Uniform Law of Large Numbers for Dependent and Heterogeneous Data Processes," Econometrica, Econometric Society, Econometric Society, vol. 57(3), pages 675-83, May.
  5. Domowitz, Ian & White, Halbert, 1982. "Misspecified models with dependent observations," Journal of Econometrics, Elsevier, Elsevier, vol. 20(1), pages 35-58, October.
  6. White, Halbert, 1980. "Nonlinear Regression on Cross-Section Data," Econometrica, Econometric Society, Econometric Society, vol. 48(3), pages 721-46, April.
  7. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 1029-54, July.
  8. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, Econometric Society, vol. 52(1), pages 143-61, January.
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Cited by:
  1. Jenish, Nazgul & Prucha, Ingmar R., 2009. "Central limit theorems and uniform laws of large numbers for arrays of random fields," Journal of Econometrics, Elsevier, Elsevier, vol. 150(1), pages 86-98, May.

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