Abstract #300244

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JSM 2003 Abstract #300244
Activity Number: 207
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #300244
Title: Maximum Likelihood Estimation for a Gradual Change Model in Exponential Families
Author(s): Ryan Gill*+
Companies: University of Louisville
Address: 328 Natural Sciences Building, Louisville, KY, 40292-0001,
Keywords: change-point model ; exponential family ; GLM ; maximum likelihood ; gradual change
Abstract:

In the classical parametric change-point model, the distribution of observed data switches abruptly at an unknown moment. However, this is impractical in many applications where the distribution parameter goes out of control and changes gradually. Therefore, a change-point model is considered in which the canonical parameter of a natural exponential family leaves its control state at an unknown moment and changes gradually. This model extends the class of generalized linear models to the case of a broken-line regression. At the same time, it develops the field of change-point analysis to a practical situation of gradual changes. It is shown that there are identifiability problems in working directly with the parameters of interest (the change-point parameter and possibly the pre-change control state and post-change slope parameter). To avoid these problems and to benefit from a more geometrically convenient perspective, maximum likelihood estimation of the canonical distribution parameters at each observation point is considered and statistical properties of these estimators are given.

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