Abstract
D.Phil. (Statistics)
We often wish to determine whether observations occurring in a natural time sequence
are from the same distribution or whether changes in distribution have taken place at
certain points in time. These time points are called change points. We study tests of the
null hypothesis of no change versus the alternative hypothesis of changes in parameter
at unknown change points, as well as point- and interval estimation of the change points.
For univariate observations we distinguish between two cases. In the one case we consider observations having known, but unequal, variances. In the second case each observation has a variance which is a function of the unknown mean. In the first case we develop graphical procedures which can be used for the detection, as well as for point- and interval estimation, of the change points. The method which we develop in the second case can be used for observations from any distribution, provided a suitable variance stabilizing transformation exists. Binomially distributed observations can be accommodated in both of these settings...