Fast maximum likelihood estimation of very large spatial autoregressive models: A characteristic polynomial approach

Oleg Smirnov, Luc Anselin

Research output: Contribution to journalArticle

112 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)301-319
Number of pages19
JournalComputational Statistics and Data Analysis
Volume35
Issue number3
DOIs
StatePublished - 2001
Externally publishedYes

Fingerprint

Maximum likelihood estimation
Spatial Model
Characteristic polynomial
Autoregressive Model
Maximum Likelihood Estimation
Polynomials
Cholesky Decomposition
Linear Complexity
Large Data
Spatial Data
Term
Likelihood Function
Linear Regression Model
Direct Method
Linear regression
Large Data Sets
Data structures
Manipulation
Computational complexity
Data Structures

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 journalArticle

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