EconBase
← All papers

Limit Theorems for Network Dependent Random Variables

Denis Kojevnikov, Vadim Marmer, Kyungchul Song

arXiv 4 Mar 2019 · Econometrics · publishedJournal of Econometrics (2020) · 36 citations (OpenAlex)

arXiv:1903.01059 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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.

Citation extraction

49
references
69
in-text mentions
51
distinct cited
3
self-citations
14,324
main-text words

appendix boundary found by appendix_command · 48% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Doukhan, P., Louhichi, S (1999) A new weak dependence condition and applications to moment inequalities1.00053100%
2Jenish, N., Prucha, I. R (2009) Central limit theorems and uniform laws of large numbers for arrays of random fields0.8434375%
3Conley, T. G (1999) GMM estimation with cross-sectional dependence0.81142100%
4Borg, I., Groenen, P. J. F (2005) Modern Multidimensional Scaling0.64422100%
5Kelejian, H. H., Prucha, I. R (2007) HAC estimation in a spatial framework0.64422100%
6Kim, M. S., Sun, Y (2011) Spatial heteroskedasticity and autocorrelation consistent estimation of covariance matrix0.64422100%
7Stein, C (1972) A bound for the error in the normal approximation to the distribution of a sum of dependent random variables0.64422100%
8Chung, F., Lu, L (2001) The diameter of sparse random graphs0.5113233%
9Johnsson, I., Moon, H. R (2019) Estimation of peer effects in endogenous social networks: Control function approach, Review of Economics and Statistics, forthco…0.51121100%
10Andrews, D. W. K (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation0.40511100%

Showing the top 10 of 51 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Graph Neural Networks for Causal Inference Under Network Confounding1.000157
2Causal Inference Under Approximate Neighborhood Interference1.00093
3Graph Neural Networks for Generalized Mundlak Estimator under Network Confounding1.00063
4Limit Theorems for Network Data without Metric Structure1.00053
5GMM and M Estimation under Network Dependence0.95075
6Normal Approximation for U-Statistics with Cross-Sectional Dependence0.946134
72101.123120.941124
8Inference in Models of Discrete Choice with Social Interactions Using Network Data0.94163
9Network Cluster-Robust Inference0.92094
10Empirical Challenges with Peers-of-Peers Instruments in the Linear-In-Means Model0.778175