| Summary: | 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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