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Functional relationships having many independent variables and errors with multivariate normal distribution

Author

Listed:
  • Dolby, G. R.
  • Freeman, T. G.

Abstract

This paper deals with maximum likelihood estimation of linear or nonlinear functional relationships assuming that replicated observations have been made on p variables at n points. The joint distribution of the pn errors is assumed to be multivariate normal. Existing results are extended in two ways: first, from known to unknown error covariance matrix; second, from the two variate to the multivariate case. For the linear relationship it is shown that the maximum likelihood point estimates are those obtained by the method of generalized least squares. The present method, however, has the advantage of supplying estimates of the asymptotic covariances of the structural parameter estimates.

Suggested Citation

  • Dolby, G. R. & Freeman, T. G., 1975. "Functional relationships having many independent variables and errors with multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 5(4), pages 466-479, December.
    • Handle: RePEc:eee:jmvana:v:5:y:1975:i:4:p:466-479
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    Citations

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    Cited by:

    1. Alexander Basilevsky, 1980. "The ratio estimator and maximum-likelihood weighted least squares regression," Quality & Quantity: International Journal of Methodology, Springer, vol. 14(3), pages 377-395, May.

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