Changepoints; Discrete time series; Hypothesis testing; Inferential models; Random sets
Hypothesis testing, which has been studied since the time of Fisher, Neyman and Pearson, is a fundamentally important task in statistics. As of now, the classical p-value has been extensively used for more than half a century. However, a number of serious drawbacks have been documented over the years. With the flourish of data science recently, there is a growing demand for better approaches. In this paper, we propose a novel method for hypothesis testing based on the inferential models by Martin and Liu. Our approach not only avoids all major weaknesses of the classical p-value but also provides considerable flexibility in perform testing. Besides, in this regard, the inferential model has some advantages over the popular Bayesian framework. As for application, the hazard rate estimation in the changepoint problem is investigated with the Down Jones index data. In particular, explicit computations are performed, and followed by a set of graphs at the changepoints.