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Minimax Risk and Uniform Convergence Rates for Nonparametric Dyadic Regression

Author

Listed:
  • 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
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    Cited by:

    1. Konrad Menzel, 2023. "Transfer Estimates for Causal Effects across Heterogeneous Sites," Papers 2305.01435, arXiv.org, revised Oct 2025.
    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).
    4. Wenqin Du & Bailey K. Fosdick & Wen Zhou, 2025. "Regression Modeling of the Count Relational Data with Exchangeable Dependencies," Papers 2502.11255, arXiv.org.

    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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