Application of local rank tests to nonparametric regression

Abstract

Let Y_i = f(x_i) + E_i\\ (1\\le i\\le n) with given covariates x_1\\lt x_2\\lt \\cdots\\lt 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 of f in various regions and to identify its local extrema.