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Regression analysis of dependent error models

Published online by Cambridge University Press:  17 April 2009

C. A. McGilchrist
C. A. McGilchrist
Affiliation:
Department of Statistics, University of New South Wales, P.O. Box 1, Kensington, N.S.W. 2033, Australia.
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Abstract

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A method of analysing the general linear regression model is described, for the case where the observations are correlated. For many applications the correlations are structured, with neighbouring observations being more strongly correlated than those some distance apart in time or space. Such correlation structures may often be assumed to belong to some class of models indexed by a small number of parameters. Estimation and inference procedures which are able to cope with a wide range of correlation models, are described and the methods are applied to problems which occur in biometry.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 2 , October 1986 , pp. 199 - 209
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Brown, R.L., Durbin, J. and Evans, J.M., “Techniques for testing the constancy of regression relationships over time”, J.R. Statist. Soc. Ser. B. 37 (1975) 149–163.Google Scholar
[2]Duncan, D.B. and Horn, S.D., “Linear dynamic recursive estimation from the viewpoint of regression analysis”, J. Amer. Statist. Assoc. 67 (1972), 815–821.Google Scholar
[3]Gleeson, A.C. and McGilchrist, C.A., “Recursive residuals on a rectangular lattice”, Biometrical 26 (1984), 675–681.CrossRefGoogle Scholar
[4]Mandelbrot, B.B. and Van Ness, J.W., “Fractional Brownian motions, fractional noises and applications”, SIAM Rev. 10 (1968), 422–437.CrossRefGoogle Scholar
[5]McGilchrist, C.A. and Knudsen, G.J., “Estimation of regression models in a field with stationary error structure”, Contributions to Statistics. Essays in Honour of Normal L. Johnson. (1983), North-Holland Publishing Co.Google Scholar
[6]McGilchrist, C.A., Sandland, R.L. and Hennessy, J.L., “Generalised inverses used in recursive estimation of the general linear model”, Austral. J. Statist. 25 (1983), 321–328.CrossRefGoogle Scholar
[7]McGilchrist, C.A., Sandland, R.L. and Hills, L.J., “Estimation in regression models with stationary, dependent errors”, Comm. Statist. A Theory Methods A10, (1981) 2563–2580.CrossRefGoogle Scholar
[8]Morettin, P.A., “The Levinson algorithm and its applications in time series analysis”, Internat. Statist. Rev. 52 (1984), 83–92.CrossRefGoogle Scholar
[9]Sallas, W.M., and Harville, D.A., “Best linear recursive estimation for mixed linear models”, J. Amer. Statist. Assoc. 76 (1982), 860–869.CrossRefGoogle Scholar
[10]Sandland, R.L. and McGilchrist, C.A., “Stochastic growth curve analysis”, Biometrics 35 (1979), 255–271.CrossRefGoogle Scholar
[11]Wilkinson, G.N., Eckert, S.R., Hancock, T.W. and Mayo, O., “Nearest neighbour (NN) analysis of field experiments (with discussion)”, J. R. Statist. Soc. Ser. B. 45 (1983), 151–211.Google Scholar