IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i20p4311-d1260878.html
   My bibliography  Save this article

Minimum Residual Sum of Squares Estimation Method for High-Dimensional Partial Correlation Coefficient

Author

Listed:
  • Jingying Yang

    (School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Guishu Bai

    (School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Mei Yan

    (School of Mathematics, Yunnan Normal University, Kunming 650500, China)

Abstract

The partial correlation coefficient (Pcor) is a vital statistical tool employed across various scientific domains to decipher intricate relationships and reveal inherent mechanisms. However, existing methods for estimating Pcor often overlook its accurate calculation. In response, this paper introduces a minimum residual sum of squares Pcor estimation method (MRSS), a high-precision approach tailored for high-dimensional scenarios. Notably, the MRSS algorithm reduces the estimation bias encountered with positive Pcor. Through simulations on high-dimensional data, encompassing both sparse and non-sparse conditions, MRSS consistently mitigates the arithmetic bias for positive Pcors, surpassing other algorithms discussed. For instance, for large sample sizes ( n ≥ 100 ) with Pcor > 0, the MRSS algorithm reduces the MSE and RMSE by about 30–70% compared to other algorithms. The robustness and stability of the MRSS algorithm is demonstrated by the sensitivity analysis with variance and sparsity parameters. Stocks data in China’s A-share market are employed to showcase the MRSS methodology’s practicality.

Suggested Citation

  • Jingying Yang & Guishu Bai & Mei Yan, 2023. "Minimum Residual Sum of Squares Estimation Method for High-Dimensional Partial Correlation Coefficient," Mathematics, MDPI, vol. 11(20), pages 1-22, October.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4311-:d:1260878
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/20/4311/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/20/4311/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Antonis A. Michis, 2022. "Multiscale Partial Correlation Clustering of Stock Market Returns," JRFM, MDPI, vol. 15(1), pages 1-22, January.
    2. Kshitij Khare & Sang-Yun Oh & Bala Rajaratnam, 2015. "A convex pseudolikelihood framework for high dimensional partial correlation estimation with convergence guarantees," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(4), pages 803-825, September.
    3. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    4. Dror Y Kenett & Michele Tumminello & Asaf Madi & Gitit Gur-Gershgoren & Rosario N Mantegna & Eshel Ben-Jacob, 2010. "Dominating Clasp of the Financial Sector Revealed by Partial Correlation Analysis of the Stock Market," PLOS ONE, Public Library of Science, vol. 5(12), pages 1-14, December.
    5. Peng, Jie & Wang, Pei & Zhou, Nengfeng & Zhu, Ji, 2009. "Partial Correlation Estimation by Joint Sparse Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 735-746.
    6. Gang-Jin Wang & Chi Xie & H. Eugene Stanley, 2018. "Correlation Structure and Evolution of World Stock Markets: Evidence from Pearson and Partial Correlation-Based Networks," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 607-635, March.
    7. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    8. Dror Y. Kenett & Xuqing Huang & Irena Vodenska & Shlomo Havlin & H. Eugene Stanley, 2015. "Partial correlation analysis: applications for financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 15(4), pages 569-578, April.
    9. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    10. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    11. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
    Full references (including those not matched with items on IDEAS)

    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. Audrino, Francesco & Tetereva, Anastasija, 2019. "Sentiment spillover effects for US and European companies," Journal of Banking & Finance, Elsevier, vol. 106(C), pages 542-567.
    2. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    3. Yize Zhao & Matthias Chung & Brent A. Johnson & Carlos S. Moreno & Qi Long, 2016. "Hierarchical Feature Selection Incorporating Known and Novel Biological Information: Identifying Genomic Features Related to Prostate Cancer Recurrence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1427-1439, October.
    4. Jie Jian & Peijun Sang & Mu Zhu, 2024. "Two Gaussian Regularization Methods for Time-Varying Networks," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(4), pages 853-873, December.
    5. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    6. Mr. Jorge A Chan-Lau, 2017. "Variance Decomposition Networks: Potential Pitfalls and a Simple Solution," IMF Working Papers 2017/107, International Monetary Fund.
    7. Victor Chernozhukov & Christian Hansen & Yuan Liao, 2015. "A lava attack on the recovery of sums of dense and sparse signals," CeMMAP working papers CWP56/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Takumi Saegusa & Tianzhou Ma & Gang Li & Ying Qing Chen & Mei-Ling Ting Lee, 2020. "Variable Selection in Threshold Regression Model with Applications to HIV Drug Adherence Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(3), pages 376-398, December.
    9. Feng Hong & Lu Tian & Viswanath Devanarayan, 2023. "Improving the Robustness of Variable Selection and Predictive Performance of Regularized Generalized Linear Models and Cox Proportional Hazard Models," Mathematics, MDPI, vol. 11(3), pages 1-13, January.
    10. Massimiliano Caporin & Francesco Poli, 2017. "Building News Measures from Textual Data and an Application to Volatility Forecasting," Econometrics, MDPI, vol. 5(3), pages 1-46, August.
    11. Pei Wang & Shunjie Chen & Sijia Yang, 2022. "Recent Advances on Penalized Regression Models for Biological Data," Mathematics, MDPI, vol. 10(19), pages 1-24, October.
    12. Justin B. Post & Howard D. Bondell, 2013. "Factor Selection and Structural Identification in the Interaction ANOVA Model," Biometrics, The International Biometric Society, vol. 69(1), pages 70-79, March.
    13. Jiang, Liewen & Bondell, Howard D. & Wang, Huixia Judy, 2014. "Interquantile shrinkage and variable selection in quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 208-219.
    14. Matthias Weber & Martin Schumacher & Harald Binder, 2014. "Regularized Regression Incorporating Network Information: Simultaneous Estimation of Covariate Coefficients and Connection Signs," Tinbergen Institute Discussion Papers 14-089/I, Tinbergen Institute.
    15. Zhiyong Huang & Ziyan Luo & Naihua Xiu, 2019. "High-Dimensional Least-Squares with Perfect Positive Correlation," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(04), pages 1-16, August.
    16. Xiaofei Wu & Rongmei Liang & Hu Yang, 2022. "Penalized and constrained LAD estimation in fixed and high dimension," Statistical Papers, Springer, vol. 63(1), pages 53-95, February.
    17. Minh Pham & Xiaodong Lin & Andrzej Ruszczyński & Yu Du, 2021. "An outer–inner linearization method for non-convex and nondifferentiable composite regularization problems," Journal of Global Optimization, Springer, vol. 81(1), pages 179-202, September.
    18. Siwei Xia & Yuehan Yang & Hu Yang, 2022. "Sparse Laplacian Shrinkage with the Graphical Lasso Estimator for Regression Problems," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 255-277, March.
    19. Yue, Mu & Li, Jialiang & Cheng, Ming-Yen, 2019. "Two-step sparse boosting for high-dimensional longitudinal data with varying coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 222-234.
    20. Kwon, Sunghoon & Oh, Seungyoung & Lee, Youngjo, 2016. "The use of random-effect models for high-dimensional variable selection problems," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 401-412.

    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:gam:jmathe:v:11:y:2023:i:20:p:4311-:d:1260878. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.