The DOI matches its Crossref record; 10 of the 10 references it cites were found in a registry or an index.
Maximum likelihood estimation of models for residual covariance in spatial regression
Abstract
We describe the maximum likelihood method for fitting the linear model when residuals are correlated and when the covariance among the residuals is determined by a parametric model containing unknown parameters. Observations are assumed to be Gaussian. We give conditions which ensure consistency and asymptotic normality of the estimators. Our main concern is with the analysis of spatial data and in this context we describe some simulation experiments to assess the small sample behaviour of estimators. We also discuss an application of the spectral approximation to the likelihood for processes on a lattice.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Ripley, B. D. (1981) · Cited by 2,819
ON STATIONARY PROCESSES IN THE PLANE
WHITTLE, P. (1954) · Biometrika · doi:10.1093/biomet/41.3-4.434 · Cited by 1,482
Application of Least Squares Regression to Relationships Containing Auto-Correlated Error Terms
Cochrane, D., & Orcutt, G. H. (1949) · Journal of the American Statistical Association · doi:10.1080/01621459.1949.10483290 · Cited by 1,376
Statistical Analysis of Stationary Time Series.
Jenkins, G. M., Grenander, U., & Rosenblatt, M. (1958) · Biometrika · doi:10.2307/2333074 · Cited by 811
An Algorithm for the Inversion of Finite Toeplitz Matrices
Trench, W. F. (1964) · Journal of the Society for Industrial and Applied Mathematics · doi:10.1137/0112045 · Cited by 557
Parameter estimation for a stationary process on a d-dimensional lattice
GUYON, X. (1982) · Biometrika · doi:10.1093/biomet/69.1.95 · Cited by 201
Errors-In-Variables Estimation for Gaussian Lattice Schemes
Besag, J. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01607.x · Cited by 172
Uniform Asymptotic Normality of the Maximum Likelihood Estimator
Sweeting, T. J. (1980) · The Annals of Statistics · doi:10.1214/aos/1176345208 · Cited by 171
Maximum-likelihood estimation in non-standard conditions
Moran, P. A. P. (1971) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100050088 · Cited by 169
On the Estimation and Testing of Spatial Interaction in Gaussian Lattice Processes
Besag, J. E., & Moran, P. A. P. (1975) · Biometrika · doi:10.1093/biomet/62.3.555 · Cited by 155
Cited by
Stein, M. L. (1999) · Springer Series in Statistics · doi:10.1007/978-1-4612-1494-6 · Cited by 2,348
Spatial data analysis: theory and practice
(2004) · Choice Reviews Online · doi:10.5860/choice.41-3486 · Cited by 965
Use of Kriging Models to Approximate Deterministic Computer Models
Martin, J. D., & Simpson, T. W. (2005) · AIAA Journal · doi:10.2514/1.8650 · Cited by 835
Anselin, L., Gallo, J. L., & Jayet, H. (2008) · Advanced Studies in Theoretical and Applied Econometrics · doi:10.1007/978-3-540-75892-1_19 · Cited by 744
Red-shifts and red herrings in geographical ecology
Lennon, J. J. (2000) · Ecography · doi:10.1034/j.1600-0587.2000.230111.x · Cited by 517
Metadata
- Authors
- MARDIA, K. V., & MARSHALL, R. J.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1984
- Volume
- 71
- Issue
- 1
- Pages
- 135-146
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2060624994
- Cited by
- 851
- References
- 10
- FWCI
- 24.12
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Maximum likelihood estimation of models for residual covariance in spatial regression. https://app.cochat.ai/papers/10.1093/biomet/71.1.135
- The paper
- MARDIA, K. V., & MARSHALL, R. J. (1984). Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika. https://doi.org/10.1093/biomet/71.1.135
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
