Date of Award


Degree Type


Degree Name

Doctor of Philosophy


This thesis presents some new results in three areas of spatial sampling when the population units are laid out in a spatial array: sample selection or treatment assignment techniques; the study of the optimality properties of these techniques when an appropriate model is assumed on the units; and parameter estimation.;For population units arranged in rectangular layouts and in layouts where either the row or column lengths are allowed to vary, some new two dimensional circular systematic sampling methods which ensure fixed sample sizes are presented, and the inclusion probabilities for each unit in these layouts are calculated.;Chapter 3 reviews various spatial correlation models which describe the spatial correlation between units arranged in a two dimensional layout. Several of these models are used in the research presented in Chapters 4 and 5.;In Chapter 4 when a spatial array of {dollar}n\sp2{dollar} spatially correlated population units arranged in a {dollar}n \times n{dollar} layout is subjected to certain constraints, it is shown that optimal methods of choosing a sample of size {dollar}n{dollar}, or of applying {dollar}n{dollar} treatments to the {dollar}n\sp2{dollar} units exist when and only when {dollar}n{dollar} = 2, 3, and 5. For other values of {dollar}n{dollar}, the efficiencies of several 'suboptimal' sampling or treatment application methods are investigated.;In Chapter 5, when the {dollar}n\sp2{dollar} spatially correlated units in the {dollar}n \times n{dollar} spatial layout are assumed to follow a Gaussian process, the multimodality of a profile log likelihood surface which is a function of both the variance and correlation parameters is investigated. Also investigated are the multimodalities of both a marginal and a concentrated log likelihood function which are functions of correlation parameters alone. The percentage of multimodal log likelihoods and the behavior of the maximum likelihood estimators of the correlation parameters are established for 1000 simulations in the cases described above. Some new ideas for establishing the convexity or nonconvexity of the concentrated likelihood function are also presented. Results vary according to the associated correlation function, the layout size {dollar}n\sp2{dollar}, and the design matrix of interest.



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