A Semi-Parametric Test for Umbrella Ordering of Binary Response Probabilities at Unknown Peak

Abstract

The Terpstra and Magel 1 multiple comparison test (referred to as the [Formula: see text] test) for umbrella alternative at unknown peak occasionally identifies false concavity in the population means. This work provides a semi-parametric test for umbrella ordering of chances of good health (free from disease) with unknown peak in a [Formula: see text] prospective study. The proposed test, a modified version of the [Formula: see text] test, determines true concavity in chances of good health more powerfully and shows low power against false concavity as compared to that of the [Formula: see text] test.