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

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  • Jenish, Nazgul
  • Prucha, Ingmar R.
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    Abstract

    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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    Bibliographic Info

    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

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    Web page: http://www.elsevier.com/locate/jeconom

    Related research

    Keywords: Random field Spatial process Central limit theorem Uniform law of large numbers Law of large numbers;

    References

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    1. Donald W.K. Andrews, 1990. "Generic Uniform Convergence," Cowles Foundation Discussion Papers 940, Cowles Foundation for Research in Economics, Yale University.
    2. Potscher, Benedikt M. & Prucha, Ingmar R., 1987. "A Uniform Law of Large Numbers for Dependent and Heterogeneous Data Process," Working Papers, C.V. Starr Center for Applied Economics, New York University 87-26, C.V. Starr Center for Applied Economics, New York University.
    3. 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.
    4. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, Econometric Society, vol. 59(4), pages 1161-67, July.
    5. 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, Elsevier, vol. 60(1-2), pages 23-63.
    6. 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.
    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, Elsevier, vol. 92(1), pages 1-45, September.
    9. 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.
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    Citations

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    Cited by:
    1. Javier Hidalgo & Myung Hwan Seo, 2013. "Specification For Lattice Processes," STICERD - Econometrics Paper Series /2013/562, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. repec:asg:wpaper:1013 is not listed on IDEAS
    3. Mullally, Conner, 2011. "Development in the Midst of Drought: Evaluating an Agricultural Extension and Credit Program in Nicaragua," 2011 Annual Meeting, July 24-26, 2011, Pittsburgh, Pennsylvania, Agricultural and Applied Economics Association 108498, Agricultural and Applied Economics Association.
    4. Elsinger, Helmut, 2013. "Comment on: A non-parametric spatial independence test using symbolic entropy," Regional Science and Urban Economics, Elsevier, vol. 43(5), pages 838-840.
    5. Qu, Xi & Lee, Lung-fei, 2013. "Locally most powerful tests for spatial interactions in the simultaneous SAR Tobit model," Regional Science and Urban Economics, Elsevier, vol. 43(2), pages 307-321.
    6. Jenish, Nazgul, 2012. "Nonparametric spatial regression under near-epoch dependence," Journal of Econometrics, Elsevier, Elsevier, vol. 167(1), pages 224-239.
    7. Jenish, Nazgul & Prucha, Ingmar R., 2012. "On spatial processes and asymptotic inference under near-epoch dependence," Journal of Econometrics, Elsevier, Elsevier, vol. 170(1), pages 178-190.
    8. El Machkouri, Mohamed & Volný, Dalibor & Wu, Wei Biao, 2013. "A central limit theorem for stationary random fields," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 123(1), pages 1-14.
    9. Debarsy, Nicolas & Ertur, Cem, 2010. "Testing for spatial autocorrelation in a fixed effects panel data model," Regional Science and Urban Economics, Elsevier, vol. 40(6), pages 453-470, November.
    10. Robinson, Peter M. & Thawornkaiwong, Supachoke, 2012. "Statistical inference on regression with spatial dependence," Journal of Econometrics, Elsevier, Elsevier, vol. 167(2), pages 521-542.
    11. Min Seong Kim & Yixiao Sun, 2012. "Asymptotic F Test in a GMM Framework with Cross Sectional Dependence," Working Papers, Ryerson University, Department of Economics 032, Ryerson University, Department of Economics.
    12. Kuersteiner, Guido M. & Prucha, Ingmar R., 2013. "Limit theory for panel data models with cross sectional dependence and sequential exogeneity," Journal of Econometrics, Elsevier, Elsevier, vol. 174(2), pages 107-126.

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