Preinerstorfer, David and Pötscher, Benedikt M. (2014): On the Power of Invariant Tests for Hypotheses on a Covariance Matrix.
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Abstract
The behavior of the power function of autocorrelation tests such as the DurbinWatson test in time series regressions or the CliffOrd test in spatial regression models has been intensively studied in the literature. When the correlation becomes strong, Krämer (1985) (for the DurbinWatson test) and Krämer (2005) (for the CliffOrd test) have shown that the power can be very low, in fact can converge to zero, under certain circumstances. Motivated by these results, Martellosio (2010) 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 serious flaws. The present paper now builds a theory as envisioned in Martellosio (2010) in a fairly 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.
Item Type:  MPRA Paper 

Original Title:  On the Power of Invariant Tests for Hypotheses on a Covariance Matrix 
Language:  English 
Keywords:  power function, invariant test, autocorrelation, spatial correlation, zeropower trap, indistinguishability, DurbinWatson test, CliffOrd test 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General 
Item ID:  61541 
Depositing User:  Benedikt Poetscher 
Date Deposited:  23 Jan 2015 14:55 
Last Modified:  27 Sep 2019 08:40 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/61541 
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On the Power of Invariant Tests for Hypotheses on a Covariance Matrix. (deposited 08 Apr 2014 05:12)
 On the Power of Invariant Tests for Hypotheses on a Covariance Matrix. (deposited 23 Jan 2015 14:55) [Currently Displayed]