On the equivalence of marginal and approximate conditional likelihoods for correlation parameters under a normal model

Marginal and approximate conditional likelihoods are obtained for the correlation parameters in a normal linear regression model with correlated errors. These likelihoods may be evaluated using the Kalman filter. It is shown that the marginal and conditional likelihoods are equivalent for any correl...

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Bibliographic Details
Published in:Biometrika 1990-12, Vol.77 (4), p.743-746
Main Author: Bellhouse, D. R.
Format: Article
Language:English
Subjects:
Autocorrelation
Correlations
Differentiable functions
Estimation methods
Exact sciences and technology
Likelihood inference
Linear inference, regression
Linear models
Mathematical functions
Mathematical independent variables
Mathematics
Maximum likelihood estimators
Parametric models
Probability and statistics
Regression analysis
Sciences and techniques of general use
Spatial correlation
Statistics
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Summary:Marginal and approximate conditional likelihoods are obtained for the correlation parameters in a normal linear regression model with correlated errors. These likelihoods may be evaluated using the Kalman filter. It is shown that the marginal and conditional likelihoods are equivalent for any correlation matrix whose entries are continuous and differentiable functions of its parameters. The results are illustrated by the application of marginal and conditional likelihood methods to estimation of the correlation param eters in time series and correlated spatial processes.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/77.4.743