Locally optimal invariant tests for change in level

Abstract

The classical change point problem is considered, from the invariance point of view. Locally optimal invariant tests are derived for the change in level, when the initial level and the common variance are assumed to be unknown. The tests derived by Chernoff and Zacks (1964) and Gardner (1969), for the change in level, when variance is known, are shown to be locally optimal invariant tests.

Keywords:

• Change point problem
• Invariance
• Wijsman's representation
• Locally best test
• Locally best unbiased test