Arbeitspapier
Minimax risk and uniform convergence rates for nonparametric dyadic regression
Let i = 1, . . . , N index a simple random sample of units drawn from some large population. For each unit we observe the vector of regressors Xi and, for each of the N (N - 1) ordered pairs of units, an outcome Yij . The outcomes Yij and Ykl are independent if their indices are disjoint, but dependent otherwise (i.e., "dyadically dependent"). Let Wij = (X'i, X'j )' ; using the sampled data we seek to construct a nonparametric estimate of the mean regression function g(Wij)=E[Yij | Xi, Xj]. 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 dw = dim(Wij ) influences the rate differently.
- Language
-
Englisch
- Bibliographic citation
-
Series: cemmap working paper ; No. CWP09/21
- Classification
-
Wirtschaft
Semiparametric and Nonparametric Methods: General
- Subject
-
Networks
Exchangeable Random Graphs
Dyadic Regression
Kernel Regression
Minimax Risk
Uniform Convergence
- Event
-
Geistige Schöpfung
- (who)
-
Graham, Bryan S.
Niu, Fengshi
Powell, James
- Event
-
Veröffentlichung
- (who)
-
Centre for Microdata Methods and Practice (cemmap)
- (where)
-
London
- (when)
-
2021
- DOI
-
doi:10.47004/wp.cem.2021.0920
- Handle
- Last update
-
10.03.2025, 11:44 AM CET
Data provider
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Arbeitspapier
Associated
- Graham, Bryan S.
- Niu, Fengshi
- Powell, James
- Centre for Microdata Methods and Practice (cemmap)
Time of origin
- 2021
Other Objects (12)
Convergence of the risk for nonparametric IV quantile regression and nonparametric IV regression with full independence
Convergence of the risk for nonparametric IV quantile regression and nonparametric IV regression with full independence
Optimal uniform convergence rates for sieve nonparametric instrumental variables regression
Nonparametric nonstationary regression
Optimal convergence rates in nonparametric regression with fractional time series errors
Optimal Convergence Rates in Nonparametric Regression with Fractional Time Series Errors
Minimax optimal designs for nonparametric regression - a further optimality property of the uniform distribution
Minimax optimal designs for nonparametric regression a further optimality property of the uniform distribution
R robustified additive nonparametric regression
Confidence regions, non-parametric regression
M Robustified Additive Nonparametric Regression
M robustified additive nonparametric regression
Convergence of the risk for nonparametric IV quantile regression and nonparametric IV regression with full independence
Convergence of the risk for nonparametric IV quantile regression and nonparametric IV regression with full independence
Optimal uniform convergence rates for sieve nonparametric instrumental variables regression
Nonparametric nonstationary regression
Optimal convergence rates in nonparametric regression with fractional time series errors
Optimal Convergence Rates in Nonparametric Regression with Fractional Time Series Errors
Minimax optimal designs for nonparametric regression - a further optimality property of the uniform distribution
Minimax optimal designs for nonparametric regression a further optimality property of the uniform distribution
R robustified additive nonparametric regression
Confidence regions, non-parametric regression
M Robustified Additive Nonparametric Regression
M robustified additive nonparametric regression
Convergence of the risk for nonparametric IV quantile regression and nonparametric IV regression with full independence
Convergence of the risk for nonparametric IV quantile regression and nonparametric IV regression with full independence
Optimal uniform convergence rates for sieve nonparametric instrumental variables regression
Nonparametric nonstationary regression
Optimal convergence rates in nonparametric regression with fractional time series errors
Optimal Convergence Rates in Nonparametric Regression with Fractional Time Series Errors
Minimax optimal designs for nonparametric regression - a further optimality property of the uniform distribution
Minimax optimal designs for nonparametric regression a further optimality property of the uniform distribution
R robustified additive nonparametric regression
Confidence regions, non-parametric regression
M Robustified Additive Nonparametric Regression