Term of Award

Spring 2010

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Department

Department of Mathematical Sciences

Committee Chair

Patricia Humphrey

Committee Member 1

Martha Abell

Committee Member 2

Greg Knofczynski

Abstract

Of interest is the specific model called the joinpoint two regime regression or broken line model composed of one regression line and a horizontal ray. This is a very restricted but highly useful subset of the well-researched change point problem. The usual approach to a more general model was first presented by Quandt (1958) who found the maximum likelihood estimates of the slope, intercept and joinpoint by assuming that the error terms are generated under the usual assumptions, that is, from a normal distribution with constant variance and are uncorrelated. We develop a method that does not rely on this assumption, demonstrate its use on an example of proximity indexes of whale cow and calf pairs, and compare the new method to the Quandt estimates in a simulation study showing this new method performs adequately.

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