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The principal correlation components estimator and its optimality

Author

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  • Wenxing Guo

    (Central University of Finance and Economics)

  • Xiaohui Liu

    (Jiangxi University of Finance and Economics)

  • Shangli Zhang

    (Beijing Jiaotong University)

Abstract

In regression analysis, the principal components regression estimator (PCRE) is often used to alleviate the effect of multicollinearity by deleting the principal components variables with smaller eigenvalues, but it has some drawbacks for subset selection. So another effective estimator based on the principal components, termed the principal correlation components estimator (PCCE), has been proposed, which selects the variables by considering the correlation coefficients between the principal components variables and the response variable. In this paper we investigate the property of the PCCE and its optimality. We prove that the PCCE is an admissible estimator and obtain the condition that the PCCE performs better than the PCRE under the balanced loss function (BLF). As an improvement of the least squares estimator (LSE), the conditions that the PCCE performs better than LSE under the BLF and the Pitman closeness criterion are derived in the paper. The empirical performance of the PCCE is demonstrated by several real and simulation data examples.

Suggested Citation

  • Wenxing Guo & Xiaohui Liu & Shangli Zhang, 2016. "The principal correlation components estimator and its optimality," Statistical Papers, Springer, vol. 57(3), pages 755-779, September.
    • Handle: RePEc:spr:stpapr:v:57:y:2016:i:3:d:10.1007_s00362-015-0678-y
    DOI: 10.1007/s00362-015-0678-y
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    References listed on IDEAS

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    1. Ogura, Toru, 2010. "A variable selection method in principal canonical correlation analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1117-1123, April.
    2. Wenxuan Zhong & Tingting Zhang & Yu Zhu & Jun S. Liu, 2012. "Correlation pursuit: forward stepwise variable selection for index models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(5), pages 849-870, November.
    3. Hadi, Ali S., 1988. "Diagnosing collinearity-influential observations," Computational Statistics & Data Analysis, Elsevier, vol. 7(2), pages 143-159, December.
    4. Wang, Song-Gui & Nyquist, Hans, 1991. "Effects on the eigenstructure of a data matrix when deleting an observation," Computational Statistics & Data Analysis, Elsevier, vol. 11(2), pages 179-188, March.
    5. Carter Hill, R. & Judge, George, 1987. "Improved prediction in the presence of multicollinearity," Journal of Econometrics, Elsevier, vol. 35(1), pages 83-100, May.
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    Cited by:

    1. Román Salmerón Gómez & Ainara Rodríguez Sánchez & Catalina García García & José García Pérez, 2020. "The VIF and MSE in Raise Regression," Mathematics, MDPI, vol. 8(4), pages 1-28, April.
    2. Ningning Xia & Zhidong Bai, 2019. "Convergence rate of eigenvector empirical spectral distribution of large Wigner matrices," Statistical Papers, Springer, vol. 60(3), pages 983-1015, June.

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