Analysis of multiple change-points in normally distributed series

Garza Venegas, Jorge Arturo (2013) Analysis of multiple change-points in normally distributed series. Maestría thesis, Universidad Autónoma de Nuevo León.

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Resumen

Paper 1: Change-Point Estimation for a Sequence of Normal Observations and Integration with Q-Charts. This is the first research regarding to change-point analysis for independent observations normally distributed. It considers the case when a single step change has occurred and distribution’s parameters (before and after change) are unknown. Development of maximum likelihood estimators (MLEs) for the change-point and parameters is the main concern as well as an integration with control charts in order to show its application in practice, with which retrospective and on-line analysis are both covered. A change is considered as one of the three different cases: (1) change only in mean parameter, (2) change only in variance parameter or (3) change in both parameters. Due to there are change-point estimators for change in mean and change in variance, comparison is done to show what estimator is recommended to use in each situation. Paper 2: Estimation of multiple change-points in time series normally distributed using a construction Heuristic and a Genetic Algorithm. This is the second research related to change-point analysis for independent observations normally distributed. It considers case when multiple step changes have occurred assuming that distribution’s parameters as well as change-point positions are unknown. Maximum Likelihood estimators for change-points as well as for parameters were developed considering three cases based on single step change problem: (1) multiple changes only in the mean, (2) multiple changes only in variance and (3) multiple changes in both parameters at the same time. Obtaining these change-points MLEs could be considered as an optimization problem, so a Construction Heuristic and a Genetic Algorithm (Evolutionary) were developed based on them. Comparison between these estimators was done in order to show their performance.

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