The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
Asymptotically Efficient Estimation of Covariance Matrices with Linear Structure
Open accessAbstract
One or more observations are made on a random vector, whose covariance matrix may be a linear combination of known symmetric matrices and whose mean vector may be a linear combination of known vectors; the coefficients of the linear combinations are unknown parameters to be estimated. Under the assumption of normality, equations are developed for the maximum likelihood estimates. These equations may be solved by an iterative method; in each step a set of linear equations is solved. If consistent estimates of $\sigma_0, \sigma_1, \cdots, \sigma_m$ are used to obtain the coefficients of the linear equations, the solution of these equations is asymptotically efficient as the number of observations on the random vector tends to infinity. This result is a consequence of a theorem that the solution of the generalized least squares equations is asymptotically efficient if a consistent estimate of the covariance matrix is used. Applications are made to the components of variance model in the analysis of variance and the finite moving average model in time series analysis.
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Cites
Time Series Analysis: Forecasting and Control
Geurts, M., Box, G. E. P., & Jenkins, G. M. (1977) · Journal of Marketing Research · doi:10.2307/3150485 · Cited by 19,186
An Introduction to Multivariate Statistical Analysis
Muirhead, R. J., & Anderson, T. W. (1986) · Journal of Business & Economic Statistics · doi:10.2307/1391399 · Cited by 9,082
Self-citationHannan, E. J. (1970) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316429 · Cited by 2,369
The Statistical Analysis of Time Series.
Anderson, T. W. (1995) · Biometrics · doi:10.2307/2532976 · Cited by 2,017
Self-citationMaximum-likelihood estimation for the mixed analysis of variance model
HARTLEY, H. O., & RAO, J. N. K. (1967) · Biometrika · doi:10.1093/biomet/54.1-2.93 · Cited by 617
Estimation and information in stationary time series
Whittle, P. (1953) · Arkiv för Matematik · doi:10.1007/bf02590998 · Cited by 558
EFFICIENT ESTIMATION OF PARAMETERS IN MOVING-AVERAGE MODELS
DURBIN, J. (1959) · Biometrika · doi:10.1093/biomet/46.3-4.306 · Cited by 401
The Estimation of Mixed Moving Average Autoregressive Systems
Hannan, E. J. (1969) · Biometrika · doi:10.1093/biomet/56.3.579 · Cited by 113
Estimation of Covariance Matrices with Linear Structure and Moving Average Processes of Finite Order
Anderson, T. W. (1971) · Cited by 17
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Cited by
Significance tests and goodness of fit in the analysis of covariance structures.
Bentler, P. M., & Bonett, D. G. (1980) · Psychological Bulletin · doi:10.1037//0033-2909.88.3.588 · Cited by 19,023
Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems
Harville, D. A. (1977) · Journal of the American Statistical Association · doi:10.1080/01621459.1977.10480998 · Cited by 2,667
Weighting for Unequal Selection Probabilities in Multilevel Models
Pfeffermann, D., Skinner, C. J., Holmes, D. J., Goldstein, H., & Rasbash, J. (1998) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/1467-9868.00106 · Cited by 438
Maximum Likelihood Computations with Repeated Measures: Application of the EM Algorithm
Laird, N., Lange, N., & Stram, D. (1987) · Journal of the American Statistical Association · doi:10.1080/01621459.1987.10478395 · Cited by 406
Linear Dependencies Represented by Chain Graphs
Cox, D. R., & Wermuth, N. (1993) · Statistical Science · doi:10.1214/ss/1177010887 · Cited by 273
Metadata
- Authors
- Anderson, T. W.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1973-01-01
- Volume
- 1
- Issue
- 1
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2004064635
- Cited by
- 269
- References
- 9
- FWCI
- 4.54
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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