Limit Theorems for Network Dependent Random Variables
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866910861661044736 |
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| author | Kojevnikov, Denis Marmer, Vadim Song, Kyungchul |
| author_facet | Kojevnikov, Denis Marmer, Vadim Song, Kyungchul |
| contents | This paper is concerned with cross-sectional dependence arising because observations are interconnected through an observed network. Following Doukhan and Louhichi (1999), we measure the strength of dependence by covariances of nonlinearly transformed variables. We provide a law of large numbers and central limit theorem for network dependent variables. We also provide a method of calculating standard errors robust to general forms of network dependence. For that purpose, we rely on a network heteroskedasticity and autocorrelation consistent (HAC) variance estimator, and show its consistency. The results rely on conditions characterized by tradeoffs between the rate of decay of dependence across a network and network's denseness. Our approach can accommodate data generated by network formation models, random fields on graphs, conditional dependency graphs, and large functional-causal systems of equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_01059 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Limit Theorems for Network Dependent Random Variables Kojevnikov, Denis Marmer, Vadim Song, Kyungchul Econometrics Methodology This paper is concerned with cross-sectional dependence arising because observations are interconnected through an observed network. Following Doukhan and Louhichi (1999), we measure the strength of dependence by covariances of nonlinearly transformed variables. We provide a law of large numbers and central limit theorem for network dependent variables. We also provide a method of calculating standard errors robust to general forms of network dependence. For that purpose, we rely on a network heteroskedasticity and autocorrelation consistent (HAC) variance estimator, and show its consistency. The results rely on conditions characterized by tradeoffs between the rate of decay of dependence across a network and network's denseness. Our approach can accommodate data generated by network formation models, random fields on graphs, conditional dependency graphs, and large functional-causal systems of equations. |
| title | Limit Theorems for Network Dependent Random Variables |
| topic | Econometrics Methodology |
| url | https://arxiv.org/abs/1903.01059 |