IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v70y2014icp116-126.html

Nonnegative-lasso and application in index tracking

Author

Listed:
  • Wu, Lan
  • Yang, Yuehan
  • Liu, Hanzhong

Abstract

This paper proposes the nonnegative-lasso method for variable selection in high dimensional sparse linear regression models with the nonnegative constraints on the coefficients. This method is an extension of Lasso and is shown to have variable selection consistency and estimation consistency under certain condition similar to Irrepresentable Condition in Lasso. To get the solution of the nonnegative-lasso, many algorithms such as Lars, coordinate decent can be used, among which multiplicative updates approach is preferred since it is faster and simpler. The constrained index tracking problem in stock market without short sales is studied in the latter part. The tracking results indicate that nonnegative-lasso can get small tracking error and is successful in assets selection.

Suggested Citation

  • Wu, Lan & Yang, Yuehan & Liu, Hanzhong, 2014. "Nonnegative-lasso and application in index tracking," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 116-126.
    • Handle: RePEc:eee:csdana:v:70:y:2014:i:c:p:116-126
    DOI: 10.1016/j.csda.2013.08.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947313003095
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2013.08.012?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
    4. Hansheng Wang & Guodong Li & Chih‐Ling Tsai, 2007. "Regression coefficient and autoregressive order shrinkage and selection via the lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 63-78, February.
    5. Brad M. Barber & Terrance Odean, 2000. "Trading Is Hazardous to Your Wealth: The Common Stock Investment Performance of Individual Investors," Journal of Finance, American Finance Association, vol. 55(2), pages 773-806, April.
    6. N. J. Jobst & M. D. Horniman & C. A. Lucas & G. Mitra, 2001. "Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 489-501.
    7. Malkiel, Burton G, 1995. "Returns from Investing in Equity Mutual Funds 1971 to 1991," Journal of Finance, American Finance Association, vol. 50(2), pages 549-572, June.
    8. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    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. Diego Vidaurre & Concha Bielza & Pedro Larrañaga, 2013. "A Survey of L1 Regression," International Statistical Review, International Statistical Institute, vol. 81(3), pages 361-387, December.
    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. Andriosopoulos, Kostas & Nomikos, Nikos, 2014. "Performance replication of the Spot Energy Index with optimal equity portfolio selection: Evidence from the UK, US and Brazilian markets," European Journal of Operational Research, Elsevier, vol. 234(2), pages 571-582.
    4. Lee, Wonyul & Liu, Yufeng, 2012. "Simultaneous multiple response regression and inverse covariance matrix estimation via penalized Gaussian maximum likelihood," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 241-255.
    5. Chenlei Leng & Minh-Ngoc Tran & David Nott, 2014. "Bayesian adaptive Lasso," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 221-244, April.
    6. Matsui, Hidetoshi, 2014. "Variable and boundary selection for functional data via multiclass logistic regression modeling," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 176-185.
    7. Osamu Komori & Shinto Eguchi & John B. Copas, 2015. "Generalized t-statistic for two-group classification," Biometrics, The International Biometric Society, vol. 71(2), pages 404-416, June.
    8. Nicolai Meinshausen & Peter Bühlmann, 2010. "Stability selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 417-473, September.
    9. G. Yi & J. Q. Shi & T. Choi, 2011. "Penalized Gaussian Process Regression and Classification for High-Dimensional Nonlinear Data," Biometrics, The International Biometric Society, vol. 67(4), pages 1285-1294, December.
    10. Wanling Xie & Hu Yang, 2023. "Group sparse recovery via group square-root elastic net and the iterative multivariate thresholding-based algorithm," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(3), pages 469-507, September.
    11. Zanhua Yin, 2020. "Variable selection for sparse logistic regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(7), pages 821-836, October.
    12. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    13. Lichun Wang & Yuan You & Heng Lian, 2015. "Convergence and sparsity of Lasso and group Lasso in high-dimensional generalized linear models," Statistical Papers, Springer, vol. 56(3), pages 819-828, August.
    14. Mingqiu Wang & Guo-Liang Tian, 2016. "Robust group non-convex estimations for high-dimensional partially linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 49-67, March.
    15. 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.
    16. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    17. Kaida Cai & Xuewen Lu & Hua Shen, 2025. "Group sparse sufficient dimension reduction: a model-free group variable selection method," Computational Statistics, Springer, vol. 40(5), pages 2323-2366, June.
    18. Kaida Cai & Hua Shen & Xuewen Lu, 2022. "Adaptive bi-level variable selection for multivariate failure time model with a diverging number of covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 968-993, December.
    19. Kock, Anders Bredahl & Callot, Laurent, 2015. "Oracle inequalities for high dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 186(2), pages 325-344.
    20. Yanfang Zhang & Chuanhua Wei & Xiaolin Liu, 2022. "Group Logistic Regression Models with l p,q Regularization," Mathematics, MDPI, vol. 10(13), pages 1-15, June.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:csdana:v:70:y:2014:i:c:p:116-126. 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/locate/csda .

    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.