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Central limit theorems and uniform laws of large numbers for arrays of random fields

  • Jenish, Nazgul
  • Prucha, Ingmar R.
Registered author(s):

    Over the last decades, spatial-interaction models have been increasingly used in economics. However, the development of a sufficiently general asymptotic theory for nonlinear spatial models has been hampered by a lack of relevant central limit theorems (CLTs), uniform laws of large numbers (ULLNs) and pointwise laws of large numbers (LLNs). These limit theorems form the essential building blocks towards developing the asymptotic theory of M-estimators, including maximum likelihood and generalized method of moments estimators. The paper establishes a CLT, ULLN, and LLN for spatial processes or random fields that should be applicable to a broad range of data processes.

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    File URL: http://www.sciencedirect.com/science/article/B6VC0-4VT0X8J-1/2/dcdd8f3a3450fd8dd7527829230c6bcc
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    Article provided by Elsevier in its journal Journal of Econometrics.

    Volume (Year): 150 (2009)
    Issue (Month): 1 (May)
    Pages: 86-98

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    Handle: RePEc:eee:econom:v:150:y:2009:i:1:p:86-98
    Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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    1. Davidson, James, 1993. "An L1-convergence theorem for heterogeneous mixingale arrays with trending moments," Statistics & Probability Letters, Elsevier, vol. 16(4), pages 301-304, March.
    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.
    3. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(03), pages 458-467, December.
    4. de Jong, Robert M., 1997. "Central Limit Theorems for Dependent Heterogeneous Random Variables," Econometric Theory, Cambridge University Press, vol. 13(03), pages 353-367, June.
    5. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(02), pages 241-257, June.
    6. Newey, W.K., 1989. "Uniform Convergence In Probability And Stochastic Equicontinuity," Papers 342, Princeton, Department of Economics - Econometric Research Program.
    7. Benedikt M. Potscher & Ingmar R. Prucha, 1994. "On the Formulation of Uniform Laws of Large Numbers: A Truncation Approach," NBER Technical Working Papers 0085, National Bureau of Economic Research, Inc.
    8. Conley, T. G., 1999. "GMM estimation with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 92(1), pages 1-45, September.
    9. Potscher, Benedikt M. & Prucha, Ingmar R., 1994. "Generic uniform convergence and equicontinuity concepts for random functions : An exploration of the basic structure," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 23-63.
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