This thesis studies the linear model, estimators of the treatment means, and opti¬mality criteria for designs and analysis of spatially arranged experiments. Four types of commonly used spatial correlation structures are discussed, and a neighbourhood of covariance matrices is investigated. Various properties about the neighbourhood are explored. When the covariance matrix of the error process is unknown, but be-longs to a neighbourhood of a covariance matrix, a modified generalized least squares estimator (GLSE) is proposed. This estimator seems more efficient than the ordinary least squares estimator in many practical applications. We also propose a criterion to find minimax designs that are efficient for a neighbourhood of correlations. When the number of plots is small, minimax designs can be computed exactly. When the number of plots is large, a simulated annealing algorithm is applied to find minimax or near minimax designs. Minimax designs for the least squares and generalized least squares estimators are compared in details. In general, we recommend using GLSE and the minimax design based on GLSE.
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/2068 |
| Date | 12 January 2010 |
| Creators | Ou, Beiyan |
| Contributors | Zhou, Julie |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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