Testing equality of functions under monotonicity constraints

Abstract

We consider the problem of testing equality of functions f_j:[a, b]→ℝ for j=1, 2, …, J on the basis of J independent samples from possibly different distributions under the assumption that the functions are monotone. We provide a uniform approach that covers testing equality of monotone regression curves, equality of monotone densities and equality of monotone hazards in the random censorship model. Two test statistics are proposed based on L₁-distances. We show that both statistics are asymptotically normal and we provide bootstrap implementations, which are shown to have critical regions with asymptotic level α.

Keywords:

• k-sample test
• L₁-distance
• asymptotic normality
• isotonic estimation
• smooth bootstrap

AMS Subject Classifications:

• 62G10
• 62G20
• 62E20

The research of Cécile Durot is partly supported by the French Agence Nationale de la Recherche [ANR 2011 BS01 010 01 projet Calibration].