Bryan S. Graham, Fengshi Niu, James L. Powell
arXiv 31 Jul 2019 · Mathematics — Statistics Theory · publishedJournal of Econometrics (2022) · 15 citations (OpenAlex)
arXiv:1907.13630 · PDF · DOI · OpenAlex · Extracted main text
We study nonparametric estimation of density functions for undirected dyadic random variables (i.e., random variables defined for all n\overset{def}{\equiv}\tbinom{N}{2} 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 first suggested by Holland and Leinhardt (1976). More unusual are the rates of convergence and asymptotic (normal) distributions of our dyadic density estimates. Specifically, 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 differs from the results for nonparametric estimation of densities and regression functions for monadic data, which generally have a slower rate of convergence than their corresponding sample mean.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Holland, P. W. & Leinhardt, S (1976) Local structure in social networks | 1.000 | 5 | 4 | 100% |
| 2 | Menzel, K (2017) Bootstrap with clustering in two or more dimensions | 1.000 | 5 | 4 | 100% |
| 3 | Newey, W. K (1994) Kernel estimation of partial means and a general variance estimator | 0.928 | 4 | 3 | 100% |
| 4 | Fafchamps, M. & Gubert, F (2007) The formation of risk sharing networks | 0.843 | 3 | 3 | 100% |
| 5 | Parzen, E (1962) On estimation of a probability density function and mode | 0.843 | 3 | 3 | 100% |
| 6 | Rosenblatt, M (1956) Remarks on some nonparametric estimates of a density function | 0.843 | 3 | 3 | 100% |
| 7 | Graham, B. S. (TBD) Handbook of Econometrics, volume 7, chapter The econometric analysis of networks self | 0.737 | 3 | 2 | 100% |
| 8 | Aronow, P. M., Samii, C., & Assenova, V. A (2017) Cluster-robust variance estimation for dyadic data | 0.644 | 2 | 2 | 100% |
| 9 | Cameron, A. C. & Miller, D. L (2014) Robust inference for dyadic data | 0.644 | 2 | 2 | 100% |
| 10 | Powell, J. L (1994) Handbook of Econometrics, volume 4, chapter Estimation of semiparametric models, (pp.\ 2443 – 2521) self | 0.644 | 2 | 2 | 100% |
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