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ON THE POWER OF INVARIANT TESTS FOR HYPOTHESES ON A COVARIANCE MATRIX

  • David Preinerstorfer (a1) and Benedikt M. Pötscher (a1)
Abstract

The behavior of the power function of autocorrelation tests such as the Durbin–Watson test in time series regressions or the Cliff-Ord test in spatial regression models has been intensively studied in the literature. When the correlation becomes strong, Krämer (1985, Journal of Econometrics 28, 363–370.) (for the Durbin–Watson test) and Krämer (2005, Journal of Statistical Planning and Inference, 128, 489–496) (for the Cliff-Ord test) have shown that power can be very low, in fact can converge to zero, under certain circumstances. Motivated by these results, Martellosio (2010, Econometric Theory, 26, 152–186) set out to build a general theory that would explain these findings. Unfortunately, Martellosio (2010) does not achieve this goal, as a substantial portion of his results and proofs suffer from nontrivial flaws. The present paper now builds a theory as envisioned in Martellosio (2010) in an even more general framework, covering general invariant tests of a hypothesis on the disturbance covariance matrix in a linear regression model. The general results are then specialized to testing for spatial correlation and to autocorrelation testing in time series regression models. We also characterize the situation where the null and the alternative hypothesis are indistinguishable by invariant tests.

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Corresponding author
*Address correspondence to David Preinerstorfer, Department of Statistics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria. e-mail: david.preinerstorfer@univie.ac.at
References
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R.A. Horn & C.R. Johnson (1985) Matrix analysis. Cambridge University Press.

T Kariya . (1980) Note on a condition for equality of sample variances in a linear model. Journal of the American Statistical Association, 75, 701703.

W. Krämer & H. Zeisel (1990) Finite sample power of linear regression autocorrelation tests. Journal of Econometrics, 43, 363372.

K Mynbaev . (2012) Distributions escaping to infinity and the limiting power of the Cliff-Ord test for autocorrelation. ISRN Probability and Statistics.

J Tillman . (1975) The power of the Durbin-Watson test. Econometrica, 43, 959974.

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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
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