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On efficient estimators of two seemingly unrelated regressions

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  • Wang, Lichun
  • Lian, Heng
  • Singh, Radhey S.

Abstract

In this paper, following the results presented in Liu's work [Liu, A.Y., 2002. Efficient estimation of two seemingly unrelated regression equations. Journal of Multivariate Analysis 82, 445-456], we first represent the Gauss-Markov estimator of the regression parameter as a matrix series, and hence we conclude that the observation vectors should appear in any efficient estimator in pairs. Second, we prove that the simpler form of the two-stage Aitken estimator is unique. Finally we generalize our results to the system of two seemingly unrelated regressions with unequal numbers of observations and briefly summarize our conclusions.

Suggested Citation

  • Wang, Lichun & Lian, Heng & Singh, Radhey S., 2011. "On efficient estimators of two seemingly unrelated regressions," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 563-570, May.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:5:p:563-570
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    References listed on IDEAS

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    1. Wang, Lichun & Veraverbeke, Noël, 2008. "MSE superiority of Bayes and empirical Bayes estimators in two generalized seemingly unrelated regressions," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 109-117, February.
    2. Foschi, Paolo & Kontoghiorghes, Erricos J., 2002. "Seemingly unrelated regression model with unequal size observations: computational aspects," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 211-229, November.
    3. Liu, Aiyi, 2002. "Efficient Estimation of Two Seemingly Unrelated Regression Equations," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 445-456, August.
    4. Schmidt, Peter, 1977. "Estimation of seemingly unrelated regressions with unequal numbers of observations," Journal of Econometrics, Elsevier, vol. 5(3), pages 365-377, May.
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    Cited by:

    1. Wang, Min & Sun, Xiaoqian, 2012. "Bayesian inference for the correlation coefficient in two seemingly unrelated regressions," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2442-2453.
    2. Tiong, Kah Yong & Ma, Zhenliang & Palmqvist, Carl-William, 2023. "Analyzing factors contributing to real-time train arrival delays using seemingly unrelated regression models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 174(C).
    3. Zhao, Li & Xu, Xingzhong, 2017. "Generalized canonical correlation variables improved estimation in high dimensional seemingly unrelated regression models," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 119-126.

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