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Activity Number:
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382
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Type:
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Contributed
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Date/Time:
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Thursday, August 15, 2002 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Nonparametric Statistics*
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| Abstract - #300487 |
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Title:
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Multivariate Spectral Analysis Using Cholesky Decomposition
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Author(s):
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Ming Dai*+ and Wensheng Guo+
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Affiliation(s):
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University of Pennsylvania and University of Pennsylvania
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Address:
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510 Blockley Hall, 423 Guardian Drive, Philadelphia, Pennsylvania, 19104, USA 613 Blockley Hall, 423 Guardian Drive, Philadelphia, PA, 19104-6021,
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Keywords:
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Bootstrap ; Cholesky decomposition ; Smoothing spline ; Spectral analysis
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Abstract:
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In multivariate spectral analysis, existing methods first calculate the periodogram and then smooth it to obtain a consistent estimate for the spectrum. In order to guarantee that the final estimate is positive definite, some constraints have to be imposed such as using the same smoothing parameter for all elements in the spectrum. This is very restrictive as different elements may have different smoothness and require different smoothing parameters. In this paper, we propose to smooth the Cholesky decomposition of the periodogram instead, which allows different smoothness for different elements. The final estimate of spectrum is reconstructed from the smoothed Cholesky elements, which is consistent and guarantees to be positive definite. More importantly, the Cholesky decomposition matrix can be used as a transfer function in generating a time series with any designed spectrum. This not only provides us much flexibility in simulations, but also allows us to construct bootstrap confidence intervals on the spectrum by generating the bootstrap sample using the estimated Cholesky decomposition matrix. A numerical example and an application to EEG data are used as illustrations.
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- The address information is for the authors that have a + after their name.
- Authors who are presenting talks have a * after their name.
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