On Mixture Alternatives and Wilcoxon’s Signed-Rank Test

2013/11/21 by Jonathan D. Rosenblatt, Jonathan Rosenblatt, Yoav Benjamini
Computer Science · Mathematics · #Affect (linguistics) #Bayesian Methods and Mixture Models #Mixture model #Nonparametric statistics #Parametric statistics #Statistical Methods and Bayesian Inference #Statistical Methods in Clinical Trials #Statistical hypothesis testing #Test (biology) #math.ST #stat.TH

paper · pdf · doi:10.1080/00031305.2017.1360795

arxiv created 2013/11/21 · openalex created_date 2016/06/24 · openalex publication_date 2017/08/01 · arxiv updated 2017/08/03 · openalex updated_date 2026/08/05

Abstract

The shift alternative model has been the canonical alternative hypothesis since the early days of statistics. This holds true both in parametric and nonparametric statistical testing. In this contribution, we argue that in several applications of interest, the shift alternative is dubious while a mixture alternative is more plausible, because the treatment is expected to affect only a subpopulation. When considering mixture hypotheses, classical tests may no longer enjoy their desirable properties. In particular, we show that the t-test may be underpowered compared to Wilcoxon’s signed-rank test, even under a Gaussian null. We consider implications to personalized medicine and medical imaging.

Citations

• Higher criticism for detecting sparse heterogeneous mixtures
• The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses
• The Probable Error of a Mean
• Microarrays, Empirical Bayes and the Two-Groups Model
• Uncovering the Hidden Risk Architecture of the Schizophrenias: Confirmation in Three Independent Genome-Wide Association Studies
• Hypothesis test for normal mixture models: The EM approach