Testing equality of functions under monotonicity constraints

2012/07/09 by Cécile Durot, Durot, Cécile, Piet Groeneboom +3
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Inference #Statistical Methods in Clinical Trials #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1207.2118

openalex publication_date 2012/07/09 · arxiv created 2013/07/01 · arxiv updated 2013/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of testing equality of functions f_j:[0,1]→ ℝ for j=1,2,...,J 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.

Citations

• Local maxima of two dependent Brownian Motions never coincide
• On a new multivariate two-sample test
• Use of Ranks in One-Criterion Variance Analysis
• Probability Tables for Individual Comparisons by Ranking Methods

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