More on the F-test under Nonspherical Disturbances

  • Walter Krämer
  • Christoph Hanck


We show that the F-test can be both liberal and conservative in the context of a particular type of nonspherical behaviour induced by spatial autocorrelation, and that the conservative variant is more likely to occur for extreme values of the spatial autocorrelation parameter. In particular, it will wipe out the progressive one as the sample size increases.


Spatial Autocorrelation Linear Regression Model Null Distribution Conservative Variant Rejection Probability 
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  1. 1.
    Anselin, L., Florax, R. (eds.): New directions in spatial econometrics. Springer, Berlin (1995)MATHGoogle Scholar
  2. 2.
    Banerjee, A.N., Magnus, J.: On the sensitivity of the usual t- and F-tests to covariance misspecifications. J. Econometrics 95, 157–176 (2000)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Hillier, O.H., King, M.L: Linear regression with correlated errors: bounds on coefficient estimates and t-values. In: King, M.L., Giles, D.E.A.(eds.) Specification Analysis in the Linear Model, pp. 74–80. Routledge and Kegan-Paul, London (1982)Google Scholar
  4. 4.
    Kiviet, J.F.: Effects of ARMA errors on tests for regression coefficients: comments on Vinod's article, improved and additional results. J. Am. Stat. Assoc. 75, 333–358 (1980)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Krämer, W.: On the robustness of the F-test to autocorrelation among disturbances. Econ. Lett. 30, 37–40 (1989)CrossRefGoogle Scholar
  6. 6.
    Krämer, W.: The robustness of the F-test to spatial autocorrelation among regression disturbances. Statistica 63, 435–440 (2003)MATHMathSciNetGoogle Scholar
  7. 7.
    Krämer, W., Kiviet, J., Breitung, J.: The null distribution of the F-test in the linear regression model with autocorrelated disturbances. Statistica 50, 503–509 (1990)MathSciNetGoogle Scholar
  8. 8.
    Vinod, H.D.: Effects of ARMA errors on the significance tests for regression coefficients. J. Am. Stat. Assoc. 71, 929–933 (1976)MATHCrossRefGoogle Scholar

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© Physica-Verlag Heidelberg 2009

Authors and Affiliations

  1. 1.Fakultät StatistikTechnische Universität DortmundDortmundGermany
  2. 2.Department Quantitative EconomicsUniversiteit MaastrichtLM MaastrichtThe Netherlands

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