IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v57y2016i3d10.1007_s00362-015-0678-y.html
   My bibliography  Save this article

The principal correlation components estimator and its optimality

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-015-0678-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00362-015-0678-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shan Luo & Zehua Chen, 2014. "Sequential Lasso Cum EBIC for Feature Selection With Ultra-High Dimensional Feature Space," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1229-1240, September.
    2. Wan, Alan T. K. & Chaturvedi, Anoop, 2001. "Double k-Class Estimators in Regression Models with Non-spherical Disturbances," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 226-250, November.
    3. Jacques Bénasséni, 2018. "A correction of approximations used in sensitivity study of principal component analysis," Computational Statistics, Springer, vol. 33(4), pages 1939-1955, December.
    4. Dong, Yuexiao & Yu, Zhou & Zhu, Liping, 2020. "Model-free variable selection for conditional mean in regression," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    5. Zhou Yu & Yuexiao Dong & Li-Xing Zhu, 2016. "Trace Pursuit: A General Framework for Model-Free Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 813-821, April.
    6. Li, Yujie & Li, Gaorong & Lian, Heng & Tong, Tiejun, 2017. "Profile forward regression screening for ultra-high dimensional semiparametric varying coefficient partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 133-150.
    7. Ryoya Oda & Hirokazu Yanagihara & Yasunori Fujikoshi, 2021. "Strong Consistency of Log-Likelihood-Based Information Criterion in High-Dimensional Canonical Correlation Analysis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 109-127, February.
    8. Hong, Hyokyoung G. & Zheng, Qi & Li, Yi, 2019. "Forward regression for Cox models with high-dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 268-290.
    9. Matthew Pritsker, 2017. "Choosing Stress Scenarios for Systemic Risk Through Dimension Reduction," Supervisory Research and Analysis Working Papers RPA 17-4, Federal Reserve Bank of Boston.
    10. Cao, Ming-Xiang & He, Dao-Jiang, 2017. "Admissibility of linear estimators of the common mean parameter in general linear models under a balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 246-254.
    11. Eric Hillebrand & Tae-Hwy Lee, 2012. "Stein-Rule Estimation and Generalized Shrinkage Methods for Forecasting Using Many Predictors," Advances in Econometrics, in: 30th Anniversary Edition, pages 171-196, Emerald Group Publishing Limited.
    12. Zhang, Xinyu & Chen, Ti & Wan, Alan T.K. & Zou, Guohua, 2009. "Robustness of Stein-type estimators under a non-scalar error covariance structure," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2376-2388, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:57:y:2016:i:3:d:10.1007_s00362-015-0678-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.