Application of local rank tests to nonparametric regression

Let Y-i = f(x(i)) + E-i (1 less than or equal to i less than or equal to n) with given covariates x(1) < x(2) < ... < x(n), an unknown regression function f and independent random errors E-i with median zero. It is shown how to apply several linear rank test statistics simultaneously in order to test monotonicity off in various regions and to identify its local extrema.