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Kernel density estimation for undirected dyadic data

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  • Bryan S. Graham

    (Institute for Fiscal Studies and University of California, Berkeley)

  • Fengshi Niu

    (Institute for Fiscal Studies)

  • James L. Powell

    (Institute for Fiscal Studies and University of California, Berkeley)

Abstract

We study nonparametric estimation of density functions for undirected dyadic random variables (i.e., random variables de?ned for all unordered pairs of agents/nodes in a weighted network of order N). These random variables satisfy a local dependence property: any random variables in the network that share one or two indices may be dependent, while those sharing no indices in common are independent. In this setting, we show that density functions may be estimated by an application of the kernel estimation method of Rosenblatt (1956) and Parzen (1962). We suggest an estimate of their asymptotic variances inspired by a combination of (i) Newey’s (1994) method of variance estimation for kernel estimators in the “monadic” setting and (ii) a variance estimator for the (estimated) density of a simple network ?rst suggested by Holland & Leinhardt (1976). More unusual are the rates of convergence and asymptotic (normal) distributions of our dyadic density estimates. Speci?cally, we show that they converge at the same rate as the (unconditional) dyadic sample mean: the square root of the number, N, of nodes. This di?ers from the results for nonparametric estimation of densities and regres-sion functions for monadic data, which generally have a slower rate of convergence than their corresponding sample mean.

Suggested Citation

  • Bryan S. Graham & Fengshi Niu & James L. Powell, 2019. "Kernel density estimation for undirected dyadic data," CeMMAP working papers CWP39/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:39/19
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    References listed on IDEAS

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    1. K. Nowicki, 1991. "Asymptotic distributions in random graphs with applications to social networks," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 45(3), pages 295-325, September.
    2. Michael D. König & Xiaodong Liu & Yves Zenou, 2019. "R&D Networks: Theory, Empirics, and Policy Implications," The Review of Economics and Statistics, MIT Press, vol. 101(3), pages 476-491, July.
    3. Aldous, David J., 1981. "Representations for partially exchangeable arrays of random variables," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 581-598, December.
    4. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 1-21, June.
    5. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
    6. Zenou, Yves, 2012. "Networks in Economics," CEPR Discussion Papers 9021, C.E.P.R. Discussion Papers.
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    Citations

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    Cited by:

    1. Luis E. Candelaria, 2020. "A Semiparametric Network Formation Model with Unobserved Linear Heterogeneity," Papers 2007.05403, arXiv.org, revised Aug 2020.
    2. Candelaria, Luis E., 2020. "A Semiparametric Network Formation Model with Unobserved Linear Heterogeneity," The Warwick Economics Research Paper Series (TWERPS) 1279, University of Warwick, Department of Economics.
    3. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2021. "Multiway empirical likelihood," Papers 2108.04852, arXiv.org, revised Aug 2024.
    4. Bryan S. Graham, 2019. "Network Data," NBER Working Papers 26577, National Bureau of Economic Research, Inc.
    5. Bryan S. Graham, 2019. "Dyadic Regression," Papers 1908.09029, arXiv.org.
    6. Harold D Chiang & Yukun Ma & Joel Rodrigue & Yuya Sasaki, 2021. "Dyadic double/debiased machine learning for analyzing determinants of free trade agreements," Papers 2110.04365, arXiv.org, revised Dec 2022.
    7. Harold D. Chiang & Bing Yang Tan, 2020. "Empirical likelihood and uniform convergence rates for dyadic kernel density estimation," Papers 2010.08838, arXiv.org, revised May 2022.
    8. Bryan S. Graham & Fengshi Niu & James L. Powell, 2020. "Minimax Risk and Uniform Convergence Rates for Nonparametric Dyadic Regression," Papers 2012.08444, arXiv.org, revised Mar 2021.
    9. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2021. "Multiway empirical likelihood," STICERD - Econometrics Paper Series 617, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    10. Bryan S. Graham, 2020. "Sparse network asymptotics for logistic regression," Papers 2010.04703, arXiv.org.
    11. Bryan S. Graham, 2019. "Network Data," CeMMAP working papers CWP71/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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