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

Oleg Smirnov, Luc Anselin

Research output: Contribution to journalArticle

116 Scopus citations

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 - Feb 24 2001

Keywords

  • Characteristic polynomial
  • Maximum likelihood estimation
  • Spatial statistics

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Fast maximum likelihood estimation of very large spatial autoregressive models: A characteristic polynomial approach'. Together they form a unique fingerprint.

  • Cite this