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Central limit theorems and uniform laws of large numbers for arrays of random fields. (English) Zbl 1429.60030

Summary: 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.

MSC:

60F05 Central limit and other weak theorems
60F15 Strong limit theorems
60G60 Random fields
62P20 Applications of statistics to economics
62M30 Inference from spatial processes
62M40 Random fields; image analysis
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