Dependence of variance on covariate design in nonparametric link regression

This paper discusses a nonparametric approach to link regression aiming at predicting a mean outcome at a link, i.e., a pair of nodes, based on currently observed data comprising covariates at nodes and outcomes at links. The variance decay rates of nonparametric link regression estimates are demonstrated to depend on covariate designs; namely, whether the covariate design is random or fixed. This covariate design-dependent nature of variance is observed in nonparametric link regression but not in conventional nonparametric regression.