Date of Award

2004

Degree Type

Thesis - Restricted

Degree Name

Master of Science (MS)

Department

Mathematics, Statistics and Computer Science

First Advisor

Bansal, Naveen

Second Advisor

Hamedani, G. G.

Third Advisor

Bajorunaite, Ruta

Abstract

Recently there has been a keen interest in the statistical analysis of change point detection and estimation. Mainly, it is because change point problems arise in many disciplines such as economics, finance, medicine, psychology, geology, literature, etc .. The awareness ofthese changes can help people to avoid unnecessary losses and to harness beneficial transitions. From the statistical point of view, a change point is a place or time point such that the observations follow one distribution up to that point and follow another distribution after that point. Usually, the statistical inference about change points has two aspects. The first is to detect if there is any change in the sequence of random variables observed. The second is to estimate corresponding location of the change point. The earliest change point study can be traced back to the 1950s. After that a good amount of articles have been published. Many of them cover the topic of single change point in the means of a sequence of independently normally distributed random variables. The frequently used methods for change point inference in the literature are the maximum likelihood ratio test, Bayesian analysis and informational approach. In my thesis, general methodologies are proposed for a single change point in a sequence of random variables from the exponential family of distributions. Special cases are also examined. The methodologies involved are mainly maximum likelihood method when the change point is a random variable and Bayesian analysis using Gibbs Sampler.

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