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Covariates in multipath change‐point problems: Modelling and consistency of the MLE

Although the single‐path change‐point problem has been extensively treated in the statistical literature, its multipath counterpart has largely been ignored. In the multipath change‐point setting, it is often of interest to assess the impact of covariates on the change point itself as well as on the parameters before and after the change point. This paper is concerned only with the inclusion of covariates in the change‐point distribution. This is achieved through the hazard of change. Maximum likelihood estimation is discussed and consistency of the maximum likelihood estimators established.