This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.
Abstract Details
Activity Number:
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136
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Type:
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Contributed
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Date/Time:
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Monday, August 2, 2010 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Statistical Computing
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Abstract - #309362 |
Title:
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Computing a Near Positive Definite Covariance Matrix from a Nonpositive Definite Matrix
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Author(s):
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Jose H. Guardiola*+ and Rachel Larreta and Pablo Tarazaga and Hassan Elsalloukh
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Companies:
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Texas A&M University and Texas A&M University and Texas A&M University and University of Arkansas at Little Rock
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Address:
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6300 Ocean Drive, Corpus Christi, TX, 78412,
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Keywords:
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Positive Definite ;
Covariance Matrix ;
Cholesky Decomposition ;
Spatial Bootstrap ;
Spatial Statistics ;
Gershgorin bounds
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Abstract:
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Covariance matrices in spatial statistics are estimated using procedures that may result in a non positive definite matrix. The estimated covariance matrix is often not suitable for further computation even that still may contain useful information. This paper proposes some methods that approximate a non-positive definite matrix to a near positive definite covariance matrix by five different methods, these methods are: the Cheng and Higham algorithm, adding a multiple of the identity, adjusting the lower Gershgorin bounds, replacing non positive eigenvalues, and substituting small diagonal entries with a tolerance. These methods produce a suitable positive definite matrix that can be used for further computations. The proposed methods are then applied to a spatial bootstrap procedure that requires a positive definite matrix and these procedures are timed and compared.
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