Signal detection using categorical temporal data

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Cannon, Ann
Major Professor
William Meeker
Noel Cressie
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In an attempt to discover differences in behavior between two groups of rats, one treated and one control, many different correlated test statistics are computed. Previously, a decision was made by determining which of the test statistics were significant. Later a single test statistic was created by counting the number of significant individual tests. This dissertation considers two areas of the analysis of the categorical temporal data that arise from experiments designed to detect differences in rat behavior;First, the spatial statistic known as the K function is adapted for temporal processes and patterns. The (optimal) K-function estimator is used in a testing procedure to determine whether behavior patterns of exposed rats versus control rats are different. Specifically, the temporal analogue to the K function is given and an approximately optimal estimator is developed. Next, a testing procedure, to determine whether a group of point patterns is generated from complete temporal randomness, is given. Finally, a testing procedure, to compare pairwise two groups of point patterns, is given. The testing procedures are illustrated with rat-behavior data from both a control-control experiment as well as an exposed-control experiment, where in the latter case a difference in behavior is known to exist;We go on to give two possible alternatives to the global statistic consisting of a count of significant tests: the sum of the squared test statistics and a Wald-like combination of the test statistics using the covariance matrix. The asymptotic null distributions of all three statistics are given, as well as a method for computing simulated distributions using the bootstrap method. The use of all three methods is then demonstrated on each of three data sets. Finally, a simulated power study reveals that the Wald-like statistic is often quite better than the other two, leading to the suggestion of its use in place of the other two Statistics and Probability;

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Sat Jan 01 00:00:00 UTC 1994