Testing monotonicity of a hazard: Asymptotic distribution theory

Monotonicity Testing

We present improved algorithms for testing monotonicity of functions. Namely, given the ability to query an unknown function f : E' -+ E, where E and E are finite ordered sets, the test always accepts a monotone f and rejects f with high probability if it is e-far from being monotone (i.e., if every monotone function differs from f on more than an E fraction of the domain). For any E > 0, the q...

Testing Monotonicity

We present a (randomized) test for monotonicity of Boolean functions. Namely, given the ability to query an unknown function at arguments of its choice, the test always accepts a monotone , and rejects with high probability if it is -far from being monotone (i.e., every monotone function differs from on more than an fraction of the domain). The complexity of the test is ! #" %$ . The analysis o...

TESTING MONOTONICITY OF REGRESSIONBy

We consider the problem of testing monotonicity of the regression function in a standard nonparametric regression model. We introduce test statistics that are functionals of a certain natural U-process. We study the limiting distribution of these test statistics through strong approximation methods and the extreme value theory for Gaussian processes. We show that the tests are consistent agains...

Testing Monotonicity of Regression

We consider the problem of testing monotonicity of the regression function in a nonparametric regression model. We introduce test statistics that are functionals of a certain natural U-process. We study the limiting distribution of these test statistics through strong approximation methods and the extreme value theory for Gaussian processes. We show that the tests are consistent against general...

Asymptotic Distribution of Divergence Measure with Applications