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Change-Point Problems in Generalized Linear Models

Hongling Zhou, Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health

Statistical models which involve change-points are termed as change-point models. The change-point problem has been one of the central issues of statistical inference for several decades. Much of the existing research is focused on change-point models with a single and abrupt change.  Literature on this topic are divided between models in which continuity is assumed and those which allow a discontinuity at the point of change. The major difficulty lies in both cases are the lack of smoothness of the likelihood with respect to the change-points. Furthermore, the change-point as a parameter disappears under the null hypothesis of no change. The major classical approaches to the change-point problem have been CUSUM procedure, likelihood and quasi-likelihood methods. I will discuss these existing approches for cross-sectional data with continuous and discrete responses under the GLM framework.