Abstract
The maximization of the log-likelihood function required in the estimation of spatial autoregressive linear regression models is a computationally intensive procedure that involves the manipulation of matrices of dimension equal to the size of the data set. Common computational approaches applied to this problem include the use of the eigenvalues of the spatial weights matrix (W), the application of Cholesky decomposition to compute the Jacobian term I - pW, and various approximations. These procedures are computationally intensive and/or require significant amounts of memory for intermediate data structures, which becomes problematic in the analysis of very large spatial data sets (tens of thousands to millions of observations). In this paper, we outline a new method for evaluating the Jacobian term that is based on the characteristic polynomial of the spatial weights matrix W. In numerical experiments, this algorithm approaches linear computational complexity, which makes it the fastest direct method currently available, especially for very large data sets.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 301-319 |
| Number of pages | 19 |
| Journal | Computational Statistics and Data Analysis |
| Volume | 35 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2001 |
| Externally published | Yes |
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Keywords
- Characteristic polynomial
- Maximum likelihood estimation
- Spatial statistics
ASJC Scopus subject areas
- Computational Theory and Mathematics
- Statistics, Probability and Uncertainty
- Electrical and Electronic Engineering
- Computational Mathematics
- Numerical Analysis
- Statistics and Probability
Cite this
Fast maximum likelihood estimation of very large spatial autoregressive models : A characteristic polynomial approach. / Smirnov, Oleg; Anselin, Luc.
In: Computational Statistics and Data Analysis, Vol. 35, No. 3, 2001, p. 301-319.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Fast maximum likelihood estimation of very large spatial autoregressive models
T2 - A characteristic polynomial approach
AU - Smirnov, Oleg
AU - Anselin, Luc
PY - 2001
Y1 - 2001
N2 - The maximization of the log-likelihood function required in the estimation of spatial autoregressive linear regression models is a computationally intensive procedure that involves the manipulation of matrices of dimension equal to the size of the data set. Common computational approaches applied to this problem include the use of the eigenvalues of the spatial weights matrix (W), the application of Cholesky decomposition to compute the Jacobian term I - pW, and various approximations. These procedures are computationally intensive and/or require significant amounts of memory for intermediate data structures, which becomes problematic in the analysis of very large spatial data sets (tens of thousands to millions of observations). In this paper, we outline a new method for evaluating the Jacobian term that is based on the characteristic polynomial of the spatial weights matrix W. In numerical experiments, this algorithm approaches linear computational complexity, which makes it the fastest direct method currently available, especially for very large data sets.
AB - The maximization of the log-likelihood function required in the estimation of spatial autoregressive linear regression models is a computationally intensive procedure that involves the manipulation of matrices of dimension equal to the size of the data set. Common computational approaches applied to this problem include the use of the eigenvalues of the spatial weights matrix (W), the application of Cholesky decomposition to compute the Jacobian term I - pW, and various approximations. These procedures are computationally intensive and/or require significant amounts of memory for intermediate data structures, which becomes problematic in the analysis of very large spatial data sets (tens of thousands to millions of observations). In this paper, we outline a new method for evaluating the Jacobian term that is based on the characteristic polynomial of the spatial weights matrix W. In numerical experiments, this algorithm approaches linear computational complexity, which makes it the fastest direct method currently available, especially for very large data sets.
KW - Characteristic polynomial
KW - Maximum likelihood estimation
KW - Spatial statistics
UR - http://www.scopus.com/inward/record.url?scp=0034746220&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0034746220&partnerID=8YFLogxK
U2 - 10.1016/S0167-9473(00)00018-9
DO - 10.1016/S0167-9473(00)00018-9
M3 - Article
AN - SCOPUS:0034746220
VL - 35
SP - 301
EP - 319
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
SN - 0167-9473
IS - 3
ER -