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Minimax Risk and Uniform Convergence Rates for Nonparametric Dyadic Regression

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  • Bryan S. Graham
  • Fengshi Niu
  • James L. Powell

Abstract

We study nonparametric regression in a setting where N(N-1) dyadic outcomes are observed for N randomly sampled units. Outcomes across dyads sharing a unit in common may be dependent (i.e., our dataset exhibits dyadic dependence). 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 dimension of the regressor vector influences the rate differently.

Suggested Citation

  • Bryan S. Graham & Fengshi Niu & James L. Powell, 2021. "Minimax Risk and Uniform Convergence Rates for Nonparametric Dyadic Regression," NBER Working Papers 28548, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:28548
    Note: TWP
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    References listed on IDEAS

    as
    1. Harold D. Chiang & Kengo Kato & Yukun Ma & Yuya Sasaki, 2022. "Multiway Cluster Robust Double/Debiased Machine Learning," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1046-1056, June.
    2. Bryan S. Graham & Fengshi Niu & James L. Powell, 2019. "Kernel Density Estimation for Undirected Dyadic Data," Papers 1907.13630, arXiv.org.
    3. 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.
    4. Bryan S. Graham, 2020. "Sparse network asymptotics for logistic regression," Papers 2010.04703, arXiv.org.
    5. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
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    Cited by:

    1. Konrad Menzel, 2023. "Transfer Estimates for Causal Effects across Heterogeneous Sites," Papers 2305.01435, arXiv.org, revised May 2024.
    2. Graham, Bryan S. & Niu, Fengshi & Powell, James L., 2024. "Kernel density estimation for undirected dyadic data," Journal of Econometrics, Elsevier, vol. 240(2).
    3. Okuno, Akifumi & Yano, Keisuke, 2023. "Dependence of variance on covariate design in nonparametric link regression," Statistics & Probability Letters, Elsevier, vol. 193(C).

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    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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