### 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 - _{p}W, 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 |

### Fingerprint

### 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

*Computational Statistics and Data Analysis*,

*35*(3), 301-319. https://doi.org/10.1016/S0167-9473(00)00018-9

**Fast maximum likelihood estimation of very large spatial autoregressive models : A characteristic polynomial approach.** / Smirnov, Oleg; Anselin, Luc.

Research output: Contribution to journal › Article

*Computational Statistics and Data Analysis*, vol. 35, no. 3, pp. 301-319. https://doi.org/10.1016/S0167-9473(00)00018-9

}

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 -