Wavelet Estimation of an Unknown Function Observed with Correlated Noise |
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Authors: | Xue Wang Andrew T A Wood |
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Institution: | 1. School of Mathematics, Statistics and Actuarial Science , University of Kent at Canterbury , Kent, UK X.Wang@kent.ac.uk;3. School of Mathematical Sciences , University of Nottingham , Nottingham, UK |
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Abstract: | Tests based on rank statistics are introduced to test for systematic changes in a sequence of independent observations. Proposed tests include a rank test analogous to the parametric likelihood ratio test and others analogous to parametric Bayes tests. The tests are usable with either one- or two-sided alternative hypotheses, and their asymptotic distributions are studied. The results of the general model are applied to two special cases, and their asymptotic distributions are also investigated. A Monte Carlo study verifies the applicability of asymptotic critical points in samples of moderate size, and other simulation studies compare power of the competing tests and their special-case versions. Finally, these tests are applied to a data set of traffic fatalities. |
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Keywords: | Bayes block shrinkage Correlation structure Durbin–Levinson algorithm Innovations algorithm Pseudo likelihood estimation |
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