Tests for monotonicity of a regression mean with guaranteed level

In this paper a nonparametric procedure for testing for monotonicity of a r egression mean with guaranteed level is proposed. The procedure is based on signs of differences of observations from the response variable. The test is calibrated against the most difficult null hypothesis, when the regressi on function is constant, and produces an exact test in this context. In gen eral, the test is conservative. The power of the test is good, and comparab le with that of other nonparametric tests. It is shown that the testing pro cedure has asymptotic power I against certain local alternatives. The metho d is also robust against heavy-tailed error distributions, and even maintai ns good power when the errors are for example Cauchy distributed. A simulat ion study is provided to demonstrate finite-sample behaviour of the testing procedure.