A Multivariate Change-Point Model for Change in Mean Vector and/or Covariance Structure

Abstract

The motivation of the current research manuscript is to provide practitioners with a multivariate-analysis tool able to detect change in the mean vector and/or covariance matrix, as well as the epoch of a change, in an independent sequence of multivariate observations. The article explores the multivariate change-point model through generalized likelihood-ratio statistics applied sequentially and adapted to repeated use. We sought an analytical result for the exact moments of the generalized likelihood ratio (GLR) statistic. The benefit flowing from this sequential adaptation is to be able to monitor short runs and unknown parameter processes while controlling their run behavior. Possible areas of application are short run processes, sequential dynamic control, ambulatory monitoring, disease monitoring, and syndromic surveillance.

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