Central limit theorems and uniform laws of large numbers for arrays of random fields
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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- 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.
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Econometric Society, vol. 57(3), pages 675-83, May.
- 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.
- 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.
- 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.
- 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.
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