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