Lei Xie

Date of Award


Degree Type


Degree Name

Doctor of Philosophy


The objective of this thesis is to develop methodology for detecting and estimating parameter changes at unknown boundaries for regression models of spatial data. This methodology has many applications including quality control, epidemiology, pharmacology, agriculture, meteorology and geology.;Statistics are derived for testing a spatial array of observations from a regression model for no change in parameters against possible alternatives involving change of parameters at unknown boundaries based on a Bayes-type approach and a locally optimal framework. These test statistics are defined in terms of set indexed partial sums of regression residuals. Limit processes are obtained for set indexed partial sums of regression residuals with i.i.d. errors and distributional results based on these processes are obtained for selected change-boundary statistics. Limit processes are derived for a matrix array of partial sums of regression residuals with stationary spatial error structure. The relationship between these procedures and those for i.i.d. errors is established. Methods are given for estimating the locations of boundaries separating spatial sets of observations which are characterized by models with different parameter sets.;This methodology is then applied to the Mercer and Hall wheat-yield data and to age-period breast cancer mortality data.



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