Threshold Estimation Using P-Values

• Activity Number: 291
• Type: Topic Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Survey Research Methods
• Author(s): Atul Mallik*+ and Moulinath Banerjee and Bodhisattva Sen
• Companies: University of Michigan and University of Michigan and Columbia University
• Keywords: baseline value ; change point ; stump function

Abstract

We seek to identify the threshold value at which a real valued function takes off from its baseline level, under regression and multiple dose-response setting. This is relevant to a broad range of problems, e.g., estimating the minimum effective dose level in certain dose-response models in pharmacology, detecting tidal disruptions in dwarf spheroidal galaxies, advent of global warming etc. An important case involves the baseline set having the form [0, d], the unknown d being the threshold. On this set, the function stays at its baseline value (minima or maxima) and then takes off. The approach involves fitting stumps to p-values obtained from tests conducted at different points/bins under the hypothesis that the function is at its baseline level. This works well owing to the fact that the p-values exhibit a dichotomous behavior. This problem has natural connections to change point estimation. The procedure is consistent under minimal conditions, involves at most one tuning parameter and is computationally easy to implement. It also attains the optimal rate of convergence under certain assumptions. The asymptotic distribution are derived and subsampling is also shown to work.