Testing Separability of Covariances for Space-Time Processes

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Title: Testing Separability of Covariances for Space-Time Processes
Author: Mitchell, Matthew William
Advisors: Dr. Marc G. Genton, Committee Co-Chair
Dr. Marcia L. Gumpertz, Committee Chair
Abstract: There are numerous methods for modeling space-time covariances. One commonly used class of models are separable covariances, where the joint space-time covariance factors into the product of a covariance function that depends only on space and a covariance function that depends only on time. This greatly reduces the number of parameters, and thus makes estimation much easier. This structure is very convenient, but there has been very little written in the literature about how to formally test for it. We propose a formal test of separability. We develop a test in the context of a replicated spatio-temporal process or more generally in the context of multivariate repeated measures (for example, several variables measured at multiple times on many subjects). The test is based on likelihood ratio statistics. When the null hypothesis of separability holds, the value of the test statistic does not depend on the type of separable model. Thus we do not need asymptotic results and give estimated distributions for the test statistic under the null hypothesis for various sample sizes. We perform simulation studies to assess the power of certain non-separable models and the effect of a non-stationary mean. Then we apply the test to a multivariate repeated measures problem. The aforementioned test only applies to independent identically distributed (i.i.d.) random variables that have a sufficient amount of experimental replication. Often in practice with space-time processes, there is only one experimental replicate. However, often spatio-temporal processes are rich in time and sparse in space. When this is the case, we create pseudo-replicates from the data and apply the test for the i.i.d. case. For these `"reps" to be approximately independent, we create "gaps" by deleting some of the pseudo-replicates. However, enough "reps" need to be retained in order to ensure sufficient power. We perform simulation studies to assess how many pseudo-replicates need to be deleted in order to obtain approximate independence. We then apply this method to the RiceFACE data set.
Date: 2002-10-16
Degree: PhD
Discipline: Statistics
URI: http://www.lib.ncsu.edu/resolver/1840.16/3127


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