In a multivariate varying-coefficient model, the response vectors Y are regressed on known functions u(X) of some explanatory variables X and the coefficients in an unknown regression matrix q(Z) depend on another set of explanatory variables Z. We provide statistical tests, called local and...

Consider a multivariate nonparametric model where the unknown vector of functions depends on two sets of explanatory variables. For a fixed level of one set of explanatory variables, we provide consistent statistical tests, called local rank tests, to determine whether the multivariate...