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Biometrika 1990 77(4):743-746; doi:10.1093/biomet/77.4.743
© 1990 by Biometrika Trust
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On the equivalence of marginal and approximate conditional likelihoods for correlation parameters under a normal model

D. R. BELLHOUSE

Department of Statistical and Actuarial Sciences, University of Western Ontario London, Ontario, Canada N6A 5B9

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.

Key Words: Autocorrelation • Likelihood inference • Spatial correlation


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