IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v140y2015icp377-394.html
   My bibliography  Save this article

On estimation in the reduced-rank regression with a large number of responses and predictors

Author

Listed:
  • Kargin, Vladislav

Abstract

We consider a multivariate linear response regression in which the number of responses and predictors is large and comparable with the number of observations, and the rank of the matrix of regression coefficients is assumed to be small. We study the distribution of singular values for the matrix of regression coefficients and for the matrix of predicted responses. For both matrices, it is found that the limit distribution of the largest singular value is a rescaling of the Tracy–Widom distribution. Based on this result, we suggest algorithms for the model rank selection and compare them with the algorithm suggested by Bunea, She and Wegkamp. Next, we design two consistent estimators for the singular values of the coefficient matrix, compare them, and derive the asymptotic distribution for one of these estimators.

Suggested Citation

  • Kargin, Vladislav, 2015. "On estimation in the reduced-rank regression with a large number of responses and predictors," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 377-394.
    • Handle: RePEc:eee:jmvana:v:140:y:2015:i:c:p:377-394
    DOI: 10.1016/j.jmva.2015.06.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X15001475
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2015.06.004?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. Jean Fortier, 1966. "Simultaneous nonlinear prediction," Psychometrika, Springer;The Psychometric Society, vol. 31(4), pages 447-455, December.
    2. Jean Fortier, 1966. "Simultaneous linear prediction," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 369-381, September.
    3. Arnold Wollenberg, 1977. "Redundancy analysis an alternative for canonical correlation analysis," Psychometrika, Springer;The Psychometric Society, vol. 42(2), pages 207-219, June.
    4. Ming Yuan & Ali Ekici & Zhaosong Lu & Renato Monteiro, 2007. "Dimension reduction and coefficient estimation in multivariate linear regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 329-346, June.
    5. Baik, Jinho & Silverstein, Jack W., 2006. "Eigenvalues of large sample covariance matrices of spiked population models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1382-1408, July.
    6. Izenman, Alan Julian, 1975. "Reduced-rank regression for the multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 5(2), pages 248-264, June.
    7. Benaych-Georges, Florent & Nadakuditi, Raj Rao, 2012. "The singular values and vectors of low rank perturbations of large rectangular random matrices," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 120-135.
    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. 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.

    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. Kargin, V. & Onatski, A., 2008. "Curve forecasting by functional autoregression," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2508-2526, November.
    2. Jos Berge, 1985. "On the relationship between Fortier's simultaneous linear prediction and van den Wollenberg's redundancy analysis," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 121-122, March.
    3. Chen, Canyi & Xu, Wangli & Zhu, Liping, 2022. "Distributed estimation in heterogeneous reduced rank regression: With application to order determination in sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    4. Couillet, Romain, 2015. "Robust spiked random matrices and a robust G-MUSIC estimator," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 139-161.
    5. Wayne DeSarbo & Heungsun Hwang & Ashley Stadler Blank & Eelco Kappe, 2015. "Constrained Stochastic Extended Redundancy Analysis," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 516-534, June.
    6. Fujikoshi, Yasunori & Sakurai, Tetsuro, 2016. "High-dimensional consistency of rank estimation criteria in multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 199-212.
    7. Ding, Xiucai & Ji, Hong Chang, 2023. "Spiked multiplicative random matrices and principal components," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 25-60.
    8. Feldman, Michael J., 2023. "Spiked singular values and vectors under extreme aspect ratios," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    9. Anna Bykhovskaya & Vadim Gorin, 2023. "High-Dimensional Canonical Correlation Analysis," Papers 2306.16393, arXiv.org, revised Aug 2023.
    10. Chao, Shih-Kang & Härdle, Wolfgang K. & Huang, Chen, 2018. "Multivariate factorizable expectile regression with application to fMRI data," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 1-19.
    11. D'Ambra, Luigi & Amenta, Pietro & D'Ambra, Antonello & de Tibeiro, Jules S., 2021. "A study of the family service expenditures and the socio-demographic characteristics via fixed marginals correspondence analysis," Socio-Economic Planning Sciences, Elsevier, vol. 73(C).
    12. Pietro Giorgio Lovaglio & Giuseppe Folloni, 2011. "The estimation of Human Capital in structural models with flexible specification," Working Papers 11, AlmaLaurea Inter-University Consortium.
    13. Goh, Gyuhyeong & Dey, Dipak K. & Chen, Kun, 2017. "Bayesian sparse reduced rank multivariate regression," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 14-28.
    14. van Dam, Ynte K. & van Trijp, Hans C.M., 2011. "Cognitive and motivational structure of sustainability," Journal of Economic Psychology, Elsevier, vol. 32(5), pages 726-741.
    15. Shih-Kang Chao & Wolfgang K. Härdle & Chen Huang, 2016. "Multivariate Factorisable Sparse Asymmetric Least Squares Regression," SFB 649 Discussion Papers SFB649DP2016-058, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    16. Kohei Yoshikawa & Shuichi Kawano, 2023. "Sparse reduced-rank regression for simultaneous rank and variable selection via manifold optimization," Computational Statistics, Springer, vol. 38(1), pages 53-75, March.
    17. Heungsun Hwang & Hye Suk & Jang-Han Lee & D. Moskowitz & Jooseop Lim, 2012. "Functional Extended Redundancy Analysis," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 524-542, July.
    18. Xinyi Zhong & Chang Su & Zhou Fan, 2022. "Empirical Bayes PCA in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 853-878, July.
    19. Shih-Kang Chao & Wolfgang K. Härdle & Ming Yuan, 2015. "Factorisable Sparse Tail Event Curves," SFB 649 Discussion Papers SFB649DP2015-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    20. Vittadini, Giorgio & Minotti, Simona C. & Fattore, Marco & Lovaglio, Pietro G., 2007. "On the relationships among latent variables and residuals in PLS path modeling: The formative-reflective scheme," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5828-5846, August.

    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:eee:jmvana:v:140:y:2015:i:c:p:377-394. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.