On spatial processes and asymptotic inference under near-epoch dependence

The development of a general inferential theory for nonlinear models with cross-sectionally or spatially dependent data has been hampered by a lack of appropriate limit theorems. To facilitate a general asymptotic inference theory relevant to economic applications, this paper first extends the notio...

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Veröffentlicht in:	Journal of econometrics Jg. 170; H. 1; S. 178 - 190
Hauptverfasser:	Jenish, Nazgul, Prucha, Ingmar R.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Netherlands Elsevier B.V 01.09.2012 Elsevier Elsevier Sequoia S.A
Schlagworte:	Asymptotic methods Central limit theorem Econometric models econometrics Economic models Economic theory Estimation Generalized method of moments GMM estimator Inference Law of large numbers Mathematical analysis Near-epoch dependent processes Nonlinear analysis nonlinear models Normality Probability theory Random fields Statistical models Stochastic processes Studies Theorems Time series time series analysis C31 C10 C21 Random fields Central limit theorem GMM estimator Law of large numbers Near-epoch dependent processes
ISSN:	0304-4076, 1872-6895
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Abstract	The development of a general inferential theory for nonlinear models with cross-sectionally or spatially dependent data has been hampered by a lack of appropriate limit theorems. To facilitate a general asymptotic inference theory relevant to economic applications, this paper first extends the notion of near-epoch dependent (NED) processes used in the time series literature to random fields. The class of processes that is NED on, say, an α-mixing process, is shown to be closed under infinite transformations, and thus accommodates models with spatial dynamics. This would generally not be the case for the smaller class of α-mixing processes. The paper then derives a central limit theorem and law of large numbers for NED random fields. These limit theorems allow for fairly general forms of heterogeneity including asymptotically unbounded moments, and accommodate arrays of random fields on unevenly spaced lattices. The limit theorems are employed to establish consistency and asymptotic normality of GMM estimators. These results provide a basis for inference in a wide range of models with spatial dependence.
AbstractList	The development of a general inferential theory for nonlinear models with cross-sectionally or spatially dependent data has been hampered by a lack of appropriate limit theorems. To facilitate a general asymptotic inference theory relevant to economic applications, this paper first extends the notion of near-epoch dependent (NED) processes used in the time series literature to random fields. The class of processes that is NED on, say, an α-mixing process, is shown to be closed under infinite transformations, and thus accommodates models with spatial dynamics. This would generally not be the case for the smaller class of α-mixing processes. The paper then derives a central limit theorem and law of large numbers for NED random fields. These limit theorems allow for fairly general forms of heterogeneity including asymptotically unbounded moments, and accommodate arrays of random fields on unevenly spaced lattices. The limit theorems are employed to establish consistency and asymptotic normality of GMM estimators. These results provide a basis for inference in a wide range of models with spatial dependence.The development of a general inferential theory for nonlinear models with cross-sectionally or spatially dependent data has been hampered by a lack of appropriate limit theorems. To facilitate a general asymptotic inference theory relevant to economic applications, this paper first extends the notion of near-epoch dependent (NED) processes used in the time series literature to random fields. The class of processes that is NED on, say, an α-mixing process, is shown to be closed under infinite transformations, and thus accommodates models with spatial dynamics. This would generally not be the case for the smaller class of α-mixing processes. The paper then derives a central limit theorem and law of large numbers for NED random fields. These limit theorems allow for fairly general forms of heterogeneity including asymptotically unbounded moments, and accommodate arrays of random fields on unevenly spaced lattices. The limit theorems are employed to establish consistency and asymptotic normality of GMM estimators. These results provide a basis for inference in a wide range of models with spatial dependence. The development of a general inferential theory for nonlinear models with cross-sectionally or spatially dependent data has been hampered by a lack of appropriate limit theorems. To facilitate a general asymptotic inference theory relevant to economic applications, this paper first extends the notion of near-epoch dependent (NED) processes used in the time series literature to random fields. The class of processes that is NED on, say, an α-mixing process, is shown to be closed under infinite transformations, and thus accommodates models with spatial dynamics. This would generally not be the case for the smaller class of α-mixing processes. The paper then derives a central limit theorem and law of large numbers for NED random fields. These limit theorems allow for fairly general forms of heterogeneity including asymptotically unbounded moments, and accommodate arrays of random fields on unevenly spaced lattices. The limit theorems are employed to establish consistency and asymptotic normality of GMM estimators. These results provide a basis for inference in a wide range of models with spatial dependence. The development of a general inferential theory for nonlinear models with cross-sectionally or spatially dependent data has been hampered by a lack of appropriate limit theorems. To facilitate a general asymptotic inference theory relevant to economic applications, this paper first extends the notion of near-epoch dependent (NED) processes used in the time series literature to random fields. The class of processes that is NED on, say, an @a-mixing process, is shown to be closed under infinite transformations, and thus accommodates models with spatial dynamics. This would generally not be the case for the smaller class of @a-mixing processes. The paper then derives a central limit theorem and law of large numbers for NED random fields. These limit theorems allow for fairly general forms of heterogeneity including asymptotically unbounded moments, and accommodate arrays of random fields on unevenly spaced lattices. The limit theorems are employed to establish consistency and asymptotic normality of GMM estimators. These results provide a basis for inference in a wide range of models with spatial dependence. All rights reserved, Elsevier The development of a general inferential theory for nonlinear models with cross-sectionally or spatially dependent data has been hampered by a lack of appropriate limit theorems. To facilitate a general asymptotic inference theory relevant to economic applications, this paper first extends the notion of near-epoch dependent (NED) processes used in the time series literature to random fields. The class of processes that is NED on, say, an α-mixing process, is shown to be closed under infinite transformations, and thus accommodates models with spatial dynamics. This would generally not be the case for the smaller class of α-mixing processes. The paper then derives a central limit theorem and law of large numbers for NED random fields. These limit theorems allow for fairly general forms of heterogeneity including asymptotically unbounded moments, and accommodate arrays of random fields on unevenly spaced lattices. The limit theorems are employed to establish consistency and asymptotic normality of GMM estimators. These results provide a basis for inference in a wide range of models with spatial dependence. [PUBLICATION ABSTRACT]
Author	Jenish, Nazgul Prucha, Ingmar R.
AuthorAffiliation	2 Department of Economics, University of Maryland, College Park, MD 20742. Tel.: 301-405-3499 1 Department of Economics, New York University, 19 West 4th Street, New York, NY 10012. Tel.: 212-998-3891
AuthorAffiliation_xml	– name: 1 Department of Economics, New York University, 19 West 4th Street, New York, NY 10012. Tel.: 212-998-3891 – name: 2 Department of Economics, University of Maryland, College Park, MD 20742. Tel.: 301-405-3499
Author_xml	– sequence: 1 givenname: Nazgul surname: Jenish fullname: Jenish, Nazgul email: nazgul.jenish@nyu.edu organization: Department of Economics, New York University, 19 West 4th Street, New York, NY 10012, United States – sequence: 2 givenname: Ingmar R. surname: Prucha fullname: Prucha, Ingmar R. email: prucha@econ.umd.edu organization: Department of Economics, University of Maryland, College Park, MD 20742, United States
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SubjectTerms	Asymptotic methods Central limit theorem Econometric models econometrics Economic models Economic theory Estimation Generalized method of moments GMM estimator Inference Law of large numbers Mathematical analysis Near-epoch dependent processes Nonlinear analysis nonlinear models Normality Probability theory Random fields Statistical models Stochastic processes Studies Theorems Time series time series analysis
Title	On spatial processes and asymptotic inference under near-epoch dependence
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