Bryan S. Graham, Fengshi Niu, James L. Powell
arXiv 15 Dec 2020 · Mathematics — Statistics Theory · 5 citations (OpenAlex)
arXiv:2012.08444 · PDF · DOI · OpenAlex · Extracted main text
Let $i=1,\ldots,N$ index a simple random sample of units drawn from some large population. For each unit we observe the vector of regressors $X_{i}$ and, for each of the $N\left(N-1\right)$ ordered pairs of units, an outcome $Y_{ij}$. The outcomes $Y_{ij}$ and $Y_{kl}$ are independent if their indices are disjoint, but dependent otherwise (i.e., "dyadically dependent"). Let $W_{ij}=\left(X_{i}',X_{j}'\right)'$; using the sampled data we seek to construct a nonparametric estimate of the mean regression function $g\left(W_{ij}\right)\overset{def}{\equiv}\mathbb{E}\left[\left.Y_{ij}\right|X_{i},X_{j}\right].$ We present two sets of results. First, we calculate lower bounds on the minimax risk for estimating the regression function at (i) a point and (ii) under the infinity norm. Second, we calculate (i) pointwise and (ii) uniform convergence rates for the dyadic analog of the familiar Nadaraya-Watson (NW) kernel regression estimator. We show that the NW kernel regression estimator achieves the optimal rates suggested by our risk bounds when an appropriate bandwidth sequence is chosen. This optimal rate differs from the one available under iid data: the effective sample size is smaller and $d_W=dim(W_{ij})$ influences the rate differently.
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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 | Hansen, B. E (2008) Uniform convergence rates for kernel estimation with dependent data | 0.909 | 8 | 3 | 75% |
| 2 | Graham, B. S (2020) Network data self | 0.811 | 4 | 2 | 100% |
| 3 | Newey, W. K (1994) Kernel estimation of partial means and a general variance estimator | 0.811 | 4 | 2 | 100% |
| 4 | Linton, O. and Nielsen, J. P (1995) A kernel method of estimating structured nonparametric regression based on marginal integration | 0.737 | 3 | 2 | 100% |
| 5 | Tsybakov, A. B (2008) Introduction to Nonparametric Estimation | 0.585 | 10 | 3 | 20% |
| 6 | Chiang, H. D., Kato, K., Ma, Y., and Sasaki, Y (2019) Multiway cluster robust double/debiased machine learning | 0.585 | 3 | 1 | 100% |
| 7 | Arcones, M. A. and Gine, E (1993) Limit theorems for $ u $-processes | 0.511 | 3 | 2 | 33% |
| 8 | Aronow, P. M., Samii, C., and Assenova, V. A (2017) Cluster–robust variance estimation for dyadic data | 0.405 | 1 | 1 | 100% |
| 9 | Graham, B. S., Niu, F., and Powell, J. L (2019) Kernel density estimation for undirected dyadic data self | 0.405 | 1 | 1 | 100% |
| 10 | Graham, B. S (2020) Sparse network asymptotics for logistic regression self | 0.405 | 1 | 1 | 100% |
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