Journal
COMPUTATIONAL STATISTICS & DATA ANALYSIS
Volume 45, Issue 2, Pages 179-196Publisher
ELSEVIER
DOI: 10.1016/S0167-9473(02)00321-3
Keywords
spatial statistics; spatial autoregression; maximum likelihood; sparse matrices; log-determinants; Chebyshev matrix determinant approximations
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To cope with the increased sample sizes stemming from geocoding and other technological innovations, this paper introduces an O(n) approximation to the log-determinant term required for likelihood-based estimation of spatial autoregressive models. It takes as a point of departure Martin's (1993) Taylor series approximation based on traces of powers of the spatial weight matrix. Using a Chebyshev approximation along with techniques to efficiently compute the initial matrix power traces results in an extremely fast approximation along with bounds on the true value of the log-determinant. Using this approach, it takes less than a second to compute the approximate log-determinant of an 890,091 x 890,091 matrix. This represents a tremendous increase in speed relative to exact computation that should allow researchers to explore much larger problems and facilitate spatial specification searches. (C) 2002 Elsevier B.V. All rights reserved.
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