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On the sensitivity of the one-sided t test to covariance misspecification

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  • Qin, Huaizhen
  • Wan, Alan T.K.
  • Zou, Guohua

Abstract

Sensitivity analysis stands in contrast to diagnostic testing in that sensitivity analysis aims to answer the question of whether it matters that a nuisance parameter is non-zero, whereas a diagnostic test ascertains explicitly if the nuisance parameter is different from zero. In this paper, we introduce and derive the finite sample properties of a sensitivity statistic measuring the sensitivity of the t statistic to covariance misspecification. Unlike the earlier work by Banerjee and Magnus [A. Banerjee, J.R. Magnus, On the sensitivity of the usual t- and F-tests to covariance misspecification, Journal of Econometrics 95 (2000) 157-176] on the sensitivity of the F statistic, the theorems derived in the current paper hold under both the null and alternative hypotheses. Also, in contrast to Banerjee and Magnus' [see the above cited reference] results on the F test, we find that the decision to accept the null using the OLS based one-sided t test is not necessarily robust against covariance misspecification and depends much on the underlying data matrix. Our results also indicate that autocorrelation does not necessarily weaken the power of the OLS based t test.

Suggested Citation

  • Qin, Huaizhen & Wan, Alan T.K. & Zou, Guohua, 2009. "On the sensitivity of the one-sided t test to covariance misspecification," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1593-1609, September.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:8:p:1593-1609
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    References listed on IDEAS

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    1. Magnus, J.R., 2002. "On the sensitivity of the t-statistic," Other publications TiSEM cc3249a4-4ce5-4d34-910e-c, Tilburg University, School of Economics and Management.
    2. Jan R. Magnus & Andrey L. Vasnev, 2007. "Local sensitivity and diagnostic tests," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 166-192, March.
    3. Banerjee, Anurag N. & Magnus, Jan R., 2000. "On the sensitivity of the usual t- and F-tests to covariance misspecification," Journal of Econometrics, Elsevier, vol. 95(1), pages 157-176, March.
    4. Banerjee, Anurag N. & Magnus, Jan R., 1999. "The sensitivity of OLS when the variance matrix is (partially) unknown," Journal of Econometrics, Elsevier, vol. 92(2), pages 295-323, October.
    5. Alan T.K. Wan & Guohua Zou & Huaizhen Qin, 2007. "On the sensitivity of the restricted least squares estimators to covariance misspecification," Econometrics Journal, Royal Economic Society, vol. 10(3), pages 471-487, November.
    6. Qin, Huaizhen & Wan, Alan T.K., 2004. "ON THE PROPERTIES OF THE t- AND F-RATIOS IN LINEAR REGRESSIONS WITH NONNORMAL ERRORS," Econometric Theory, Cambridge University Press, vol. 20(4), pages 690-700, August.
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    Cited by:

    1. Magnus, Jan R. & Vasnev, Andrey L., 2015. "Interpretation and use of sensitivity in econometrics, illustrated with forecast combinations," International Journal of Forecasting, Elsevier, vol. 31(3), pages 769-781.

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