Testing change-points with linear trend

Abstract

Tests based on rank statistics are introduced to test for systematic changes in a sequence of independent observations. Proposed tests include a rank test analogous to the parametric likelihood ratio test and others analogous to parametric Bayes tests. The tests are usable with either one- or two-sided alternative hypotheses, and their asymptotic distributions are studied. The results of the general model are applied to two special cases, and their asymptotic distributions are also investigated. A Monte Carlo study verifies the applicability of asymptotic critical points in samples of moderate size, and other simulation studies compare power of the competing tests and their special-case versions. Finally, these tests are applied to a data set of traffic fatalities.

Keywords:

• change-point problem
• smooth change model
• rank tests
• Nonparametric statistics
• Bayes test
• likelihood ratio
• asymptotic distribution
• Brownian bridge process
• power comparison of tests
• simulation