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Mean square error matrix comparison of some estimators in linear regressions with multicollinearity

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  • Sarkar, Nityananda

Abstract

The ordinary least squares, the principal components regression and the ordinary ridge regression estimators are special cases of the r - k class estimator proposed by Baye and Parker (1984) for regression models with multicollinearity. We obtain necessary and sufficient conditions for the superiority of the r - k class estimator over each of these three estimators by the criterion of mean square error matrix. We also suggest tests to verify if these conditions are indeed satisfied.

Suggested Citation

  • Sarkar, Nityananda, 1996. "Mean square error matrix comparison of some estimators in linear regressions with multicollinearity," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 133-138, October.
    • Handle: RePEc:eee:stapro:v:30:y:1996:i:2:p:133-138
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    References listed on IDEAS

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    1. P.A. Bekker & H. Neudecker, 1989. "Albert's theorem applied to problems of efficiency and MSE superiority," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 43(3), pages 157-167, September.
    2. Nityananda Sarkar, 1989. "Comparisons among some estimators in misspecified linear models with multicollinearity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(4), pages 717-724, December.
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    Cited by:

    1. Özkale, M. Revan & KaçIranlar, Selahattin, 2007. "Superiority of the r-d class estimator over some estimators by the mean square error matrix criterion," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 438-446, February.
    2. Roozbeh, Mahdi, 2018. "Optimal QR-based estimation in partially linear regression models with correlated errors using GCV criterion," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 45-61.
    3. Shalini Chandra & Gargi Tyagi, 2017. "On the Performance of Some Biased Estimators in a Misspecified Model with Correlated Regressors," Statistics in Transition New Series, Polish Statistical Association, vol. 18(1), pages 27-52, March.
    4. Shalini Chandra & Nityananda Sarkar, 2015. "Comparison of the r - (k, d) Class Estimator with some Estimators for Multicollinearity under the Mahalanobis Loss Function," International Econometric Review (IER), Econometric Research Association, vol. 7(1), pages 1-12, April.
    5. Gülesen Üstündagˇ Şiray & Selahattin Kaçıranlar & Sadullah Sakallıoğlu, 2014. "r − k Class estimator in the linear regression model with correlated errors," Statistical Papers, Springer, vol. 55(2), pages 393-407, May.
    6. Deniz Inan, 2015. "Combining the Liu-type estimator and the principal component regression estimator," Statistical Papers, Springer, vol. 56(1), pages 147-156, February.
    7. Xinfeng Chang & Hu Yang, 2012. "Combining two-parameter and principal component regression estimators," Statistical Papers, Springer, vol. 53(3), pages 549-562, August.
    8. Chandra Shalini & Tyagi Gargi, 2017. "On the Performance of Some Biased Estimators in a Misspecified Model with Correlated Regressors," Statistics in Transition New Series, Polish Statistical Association, vol. 18(1), pages 27-52, March.

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    1. Shalini Chandra & Gargi Tyagi, 2017. "On the Performance of Some Biased Estimators in a Misspecified Model with Correlated Regressors," Statistics in Transition New Series, Polish Statistical Association, vol. 18(1), pages 27-52, March.
    2. Chandra Shalini & Tyagi Gargi, 2017. "On the Performance of Some Biased Estimators in a Misspecified Model with Correlated Regressors," Statistics in Transition New Series, Polish Statistical Association, vol. 18(1), pages 27-52, March.

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