title: Detecting discontinuities using nonparametric smoothing techniques in correlated data
Creators: name: Yap, Christina
Publisher: name: University of Glasgow
Year: 2004
Subjects: subject: Pure sciences, discontinuous functions, regression analysis.

description: There is increasing interest in the detection and estimation of discontinuities in regression problems with one and two covariates, due to its wide variety of applications. Moreover, in many real life applications, we are likely to encounter a certain degree of dependence in observations that are collected over time or space. Detecting changes in dependent data in the presence of a smoothly varying trend, is a much more complicated problem that previously has not been adequately studied. Hence, the aim of this thesis is to respond to the immense need for a nonparametric discontinuity test which is capable of incorporating robust estimation of the underlying dependence structure (if unknown) into the test procedure in one and two dimensions. By means of a difference-based method, using a local linear kernel smoothing technique, a global test of the hypothesis that an abrupt change is present in the smoothly varying mean level of a sequence of correlated data is developed in the one-dimensional setting. Accurate distributional calculations for the test statistic can be performed, using standard results on quadratic forms. Extensive simulations are carried out to examine the performance of the test in the cases both of correlation known and unknown. For the latter, the effectiveness of the different algorithms that have been devised to incorporate the estimation of correlation, for both the equally and unequally spaced designs, is investigated. Various factors that affect the size and power of the test are also explored. In addition, a small simulation study is performed to compare the proposed test with an isotonic regression test proposed by Wu et al. (2001). The utility of the techniques is demonstrated by applying the proposed discontinuity test to three sets of real-life data, namely the Argentina rainfall data, the global warming data and the River Clyde data. The analysis of the results are compared to those using the isotonic regression test of Wu et al. (2001) and the Bayesian test of Thomas (2001). Finally, the test is also extended to detect discontinuities in spatially correlated data. The same differencing principle as in the one-dimensional case is utilised here. However, the discontinuity in this context does not occur only at a point but over a smooth curve. Hence, the test has to take into account the additional element of direction. A two stage algorithm which makes use of a partitioning process to remove observations that are near the discontinuity curve is proposed. A motivating application for the approach is the analysis of radiometric data on cesium fallout in a particular area in Finland after a nuclear reactor accident in Chernobyl. The procedures outlined for both the one and two dimensional settings are particularly useful and relatively easy to implement. Although the main focus of the work is not to identify the exact locations of the discontinuities, useful graphical tools have been employed to infer their likely locations. The dissertation closes with a summary and discussion of the results presented, and proposes potential future work in this area.