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Activity Number:
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291
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Type:
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Contributed
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Date/Time:
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Tuesday, August 8, 2006 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Nonparametric Statistics
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| Abstract - #306658 |
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Title:
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Multivariate Time-Dependent Spectral Analysis Using Cholesky
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Author(s):
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Ming Dai*+ and Wensheng Guo
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Companies:
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The University of North Carolina at Charlotte and University of Pennsylvania
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Address:
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9201 University Blvd., Charlotte, NC, 28213,
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Keywords:
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bootstrap ; Cholesky decomposition ; locally stationary time series ; smoothing spline ; spectral analysis
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Abstract:
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In this paper, we propose a nonparametric method to analyze the spectrum of a multivariate locally stationary process. In order to ensure that the final spectral estimate is positive definite while allowing enough flexibility each of its elements, we propose to smooth the Cholesky decomposition of an initial spectral estimate and the final estimate is reconstructed from the smoothed Cholesky elements. The final estimate is smooth in time and frequency, has a global interpretation, and is consistent and positive definite. We show that the Cholesky decomposition of the spectrum can be used as a transfer function to generate a locally stationary time series with the designed spectrum. This not only provides us much flexibility in simulations, but also allows us to construct bootstrap confidence intervals. A numerical example and an application to an EEG data set are used as illusions.
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