a property of remaining unchanged regardless of changes in the conditions of measurement
In particular, statistical models that are closed under a class of transformations are called invariant. Often this invariance has important implications for inferential problems associated with the model. The principle of invariance asserts that whenever a problem is invariant under a group of transformations, then the solution to the problem should also be invariant. Applications of this principle occur in both estimation and hypothesis-testing problems. For example, maximum-likelihood estimators and likelihood-ratio tests are invariant solutions to inference problems when the model is invariant.
