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On Small Sample Properties of R2 in a Linear Regression Model with Multivariate t Errors and Proxy Variables

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  • Ohtani, Kazuhiro
  • Hasegawa, Hikaru

Abstract

In this paper we consider the small sample properties of the coefficient of determination in a linear regression model with multivariate t errors when proxy variables are used instead of unobservable regressors. The results show that if the unobservable variable is an important variable, the adjusted coefficient of determination can be more unreliable in small samples than the unadjusted coefficient of determination from both viewpoints of the bias and the MSE.

Suggested Citation

  • Ohtani, Kazuhiro & Hasegawa, Hikaru, 1993. "On Small Sample Properties of R2 in a Linear Regression Model with Multivariate t Errors and Proxy Variables," Econometric Theory, Cambridge University Press, vol. 9(3), pages 504-515, June.
    • Handle: RePEc:cup:etheor:v:9:y:1993:i:03:p:504-515_00
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    Cited by:

    1. Akio Namba & Kazuhiro Ohtani, 2007. "Risk comparison of the Stein-rule estimator in a linear regression model with omitted relevant regressors and multivariatet errors under the Pitman nearness criterion," Statistical Papers, Springer, vol. 48(1), pages 151-162, January.
    2. Ohtani, Kazuhiro, 2000. "Bootstrapping R2 and adjusted R2 in regression analysis," Economic Modelling, Elsevier, vol. 17(4), pages 473-483, December.
    3. Nadarajah Saralees, 2007. "A Truncated Bivariate t Distribution," Stochastics and Quality Control, De Gruyter, vol. 22(2), pages 303-313, January.
    4. Namba, Akio & Ohtani, Kazuhiro, 2006. "PMSE performance of the Stein-rule and positive-part Stein-rule estimators in a regression model with or without proxy variables," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 898-906, May.
    5. Cheng, C.-L. & Shalabh, & Garg, G., 2016. "Goodness of fit in restricted measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 101-116.
    6. Akio Namba, 2001. "MSE performance of the 2SHI estimator in a regression model with multivariate t error terms," Statistical Papers, Springer, vol. 42(1), pages 81-96, January.
    7. Cheng, C.-L. & Shalabh, & Garg, G., 2014. "Coefficient of determination for multiple measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 137-152.

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