A Multiple Decision Theory Analysis of Structural Stability in Regression

Using the theory of multiple decisions, this paper conducts an analysis of structural stability in location and variance for the linear-regression model. It shows that both cusum and cusum-of-squares techniques are in certain senses optimal. However, the same tests are optimal for changes in location and variance. It is also shown that there is an inherent contradiction between the use of recursive residuals and cusum techniques. The concept of a localized Bayes rule is introduced.