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Some Geometry for the Maximal Invariant in Linear Regression

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  • Patrick Marsh

Abstract

The maximal invariant forms the basis of a well established theory on hypothesis testing on the covariance structure in linear regression, see Lehman (1997). This paper examines the geometry of the maximal invariant. In particular it derives explicit expressions for both Fisher information and statistical curvature, see Efron (1975). The results apply for any sample size, for any sufficiently differentiable covariance structure and across a variety of sample densities. The results are illustrated for regressions involving autoregressive and moving average errors. Specifically, the effects of different specifications of the mean and of non-stationarity and non-invertibility may be quantified.

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  • Patrick Marsh, "undated". "Some Geometry for the Maximal Invariant in Linear Regression," Discussion Papers 04/07, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:04/07
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    References listed on IDEAS

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    1. Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, vol. 51(1), pages 153-174, January.
    2. Jones, M. C., 1987. "On moments of ratios of quadratic forms in normal variables," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 129-136, November.
    3. Ghazal, G. A., 1996. "Recurrence formula for expectations of products of quadratic forms," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 101-109, April.
    4. King, M L & Giles, D E A, 1977. "A Note on Wallis' Bounds Test and Negative Autocorrelation," Econometrica, Econometric Society, vol. 45(4), pages 1023-1026, May.
    5. Nalini Ravishanker & Edward L. Melnick & Chih‐Ling Tsai, 1990. "Differential Geometry Of Arma Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(3), pages 259-274, May.
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    Cited by:

    1. Robert L. Paige & P. Harshini Fernando, 2008. "Robust Inference in Conditionally Linear Nonlinear Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(1), pages 158-168, March.

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    Keywords

    Differential geometry; Efron curvature; Fisher information; maximal invariant;
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