Dissertation
Asymptotic study of the change-point MLE under contiguous change and its applications
Washington State University
Doctor of Philosophy (PhD), Washington State University
08/2010
DOI:
https://doi.org/10.7273/000006167
Abstract
This thesis studied the change point problem under the contiguous setup. Specifically when the amount of change is a function of the sample size and goes to zero in a smooth fashion as the sample size goes to infinity, it yields a contiguous change-point model. Two scenarios are considered: first the problem of estimating an unknown change-point in the mean vector and/or covariance matrix of a sequence of independent multivariate Gaussian random variables is considered; secondly, the research have been extended to the change-point in the parameters of a sequence of independent time-series d-dimensional-valued random variables from a general parametric family of distributions. Adapting the estimation methodology that Hinkley pursued for the case of abrupt changes, we develop theory for deriving the asymptotic distribution of the maximum likelihood estimator of the change-point for both scenarios. We also show that the rate of convergence of the change-point mle from finite samples to infinite samples is of geometric order. Extensive simulations have been performed to illustrate the closeness of the asymptotic distribution with the empirical distribution, and to evaluate its robustness to departures from normality for reasonable sample sizes as well as parameter changes. Finally, we apply the methodology to estimate the change-point in the daily log-returns data of some stock prices from NYSE. We also applied the approach to the central England temperature data to evaluate the trend of global warming.
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Details
- Title
- Asymptotic study of the change-point MLE under contiguous change and its applications
- Creators
- Li Tan
- Contributors
- Stergios B. Fotopoulos (Chair)Venkata Krishna Jandhyala (Committee Member) - Washington State University, Department of Mathematics and StatisticsHarry J Turtle (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Carson College of Business
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 135
- Identifiers
- 99901055029001842
- Language
- English
- Resource Type
- Dissertation