Minimax Risk and Uniform Convergence Rates for Nonparametric Dyadic Regression

Bryan Graham, Fengshi Niu and James Powell

No 28548, NBER Working Papers from National Bureau of Economic Research, Inc

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.

JEL-codes: C14 (search for similar items in EconPapers)
Date: 2021-03
New Economics Papers: this item is included in nep-ore
Note: TWP
References: Add references at CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.nber.org/papers/w28548.pdf (application/pdf)

Related works:
Working Paper: Minimax Risk and Uniform Convergence Rates for Nonparametric Dyadic Regression (2021)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nbr:nberwo:28548

Ordering information: This working paper can be ordered from
http://www.nber.org/papers/w28548

Access Statistics for this paper

More papers in NBER Working Papers from National Bureau of Economic Research, Inc National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.. Contact information at EDIRC.
Bibliographic data for series maintained by ().