Detecting Changes under Multivariate Normal Distributions via the Generalized Inference

Abstract

It is commonly encountered in many fields to detect whether a change occurs on a population after a special process. Based on observations for describing the population before and after the process, we formulate this problem as two statistical hypotheses testing problems within a framework of multivariate statistical analysis and then propose a generalized inference approach to solve them. The corresponding generalized $p$ values and their calculation details are provided. The proposed method is also extended to multiple testing problems. Simulation studies show that the proposed $p$ values have satisfactory frequentist performance. We illustrate our methods with a real application in manufacturing of bearings that are used in medical devices.