IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v73y2021i1d10.1007_s10463-019-00745-z.html
   My bibliography  Save this article

Clustering of subsample means based on pairwise L1 regularized empirical likelihood

Author

Listed:
  • Quynh Van Nong

    (Thai Nguyen University of Education)

  • Chi Tim Ng

    (Chonnam National University)

Abstract

To classify a vast amount of strata or subsamples with unknown families of distributions according to their strata-means, a clustering approach is developed based on pairwise $$L_1$$ L 1 regularized empirical likelihood. Under such a clustering approach, all possible contradictory conclusions are ruled out automatically. On the contrary, the decision rules based on many existing pairwise comparison procedures can generate contradictory results. Moreover, under certain mild conditions, the proposed clustering method enjoys the consistency property that with probability going to one, all strata are classified correctly. An exterior point algorithm is presented for the clustering. The applications of the proposed methods are demonstrated using stock market data and microarray data of breast cancer patients.

Suggested Citation

  • Quynh Van Nong & Chi Tim Ng, 2021. "Clustering of subsample means based on pairwise L1 regularized empirical likelihood," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 135-174, February.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:1:d:10.1007_s10463-019-00745-z
    DOI: 10.1007/s10463-019-00745-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-019-00745-z
    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/s10463-019-00745-z?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. Elena Andreou & Eric Ghysels, 2002. "Detecting multiple breaks in financial market volatility dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 579-600.
    2. Rogalski, Richard J, 1984. "New Findings Regarding Day-of-the-Week Returns over Trading and Non-trading Periods: A Note," Journal of Finance, American Finance Association, vol. 39(5), pages 1603-1614, December.
    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. Hansheng Wang & Bo Li & Chenlei Leng, 2009. "Shrinkage tuning parameter selection with a diverging number of parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 671-683, June.
    5. J. Andrew Coutts & Peter Hayes, 1999. "The weekend effect, the Stock Exchange Account and the Financial Times Industrial Ordinary Shares Index: 1987-1994," Applied Financial Economics, Taylor & Francis Journals, vol. 9(1), pages 67-71.
    6. Yingying Fan & Cheng Yong Tang, 2013. "Tuning parameter selection in high dimensional penalized likelihood," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 531-552, June.
    7. Romano Joseph P. & Shaikh Azeem & Wolf Michael, 2011. "Consonance and the Closure Method in Multiple Testing," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-25, February.
    8. 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.
    9. Chenlei Leng & Cheng Yong Tang, 2012. "Penalized empirical likelihood and growing dimensional general estimating equations," Biometrika, Biometrika Trust, vol. 99(3), pages 703-716.
    10. Jing, Bing-Yi, 1995. "Two-sample empirical likelihood method," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 315-319, September.
    11. Geman Donald & d'Avignon Christian & Naiman Daniel Q. & Winslow Raimond L., 2004. "Classifying Gene Expression Profiles from Pairwise mRNA Comparisons," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-22, August.
    12. Liu, Yukun & Zou, Changliang & Zhang, Runchu, 2008. "Empirical likelihood for the two-sample mean problem," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 548-556, April.
    13. French, Kenneth R., 1980. "Stock returns and the weekend effect," Journal of Financial Economics, Elsevier, vol. 8(1), pages 55-69, March.
    14. Alan Agresti & Matilde Bini & Bruno Bertaccini & Euijung Ryu, 2008. "Simultaneous Confidence Intervals for Comparing Binomial Parameters," Biometrics, The International Biometric Society, vol. 64(4), pages 1270-1275, December.
    15. Steeley, James M., 2001. "A note on information seasonality and the disappearance of the weekend effect in the UK stock market," Journal of Banking & Finance, Elsevier, vol. 25(10), pages 1941-1956, October.
    16. Cheng Yong Tang & Chenlei Leng, 2010. "Penalized high-dimensional empirical likelihood," Biometrika, Biometrika Trust, vol. 97(4), pages 905-920.
    17. Wang, Hansheng & Leng, Chenlei, 2007. "Unified LASSO Estimation by Least Squares Approximation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1039-1048, September.
    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. Chatzitzisi, Evanthia & Fountas, Stilianos & Panagiotidis, Theodore, 2021. "Another look at calendar anomalies," The Quarterly Review of Economics and Finance, Elsevier, vol. 80(C), pages 823-840.
    2. Fan, Rui & Lee, Ji Hyung & Shin, Youngki, 2023. "Predictive quantile regression with mixed roots and increasing dimensions: The ALQR approach," Journal of Econometrics, Elsevier, vol. 237(2).
    3. Tang, Niansheng & Yan, Xiaodong & Zhao, Puying, 2018. "Exponentially tilted likelihood inference on growing dimensional unconditional moment models," Journal of Econometrics, Elsevier, vol. 202(1), pages 57-74.
    4. Zhang, Jia & Shi, Haoming & Tian, Lemeng & Xiao, Fengjun, 2019. "Penalized generalized empirical likelihood in high-dimensional weakly dependent data," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 270-283.
    5. Xia Chen & Liyue Mao, 2020. "Penalized empirical likelihood for partially linear errors-in-variables models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 597-623, December.
    6. Lenka Zbonakova & Wolfgang Karl Härdle & Weining Wang, 2016. "Time Varying Quantile Lasso," SFB 649 Discussion Papers SFB649DP2016-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    7. Caner, Mehmet & Fan, Qingliang, 2015. "Hybrid generalized empirical likelihood estimators: Instrument selection with adaptive lasso," Journal of Econometrics, Elsevier, vol. 187(1), pages 256-274.
    8. Cho, Young-Hyun & Linton, Oliver & Whang, Yoon-Jae, 2007. "Are there Monday effects in stock returns: A stochastic dominance approach," Journal of Empirical Finance, Elsevier, vol. 14(5), pages 736-755, December.
    9. Zhang, Ting & Wang, Lei, 2020. "Smoothed empirical likelihood inference and variable selection for quantile regression with nonignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    10. Fei Jin & Lung-fei Lee, 2018. "Lasso Maximum Likelihood Estimation of Parametric Models with Singular Information Matrices," Econometrics, MDPI, vol. 6(1), pages 1-24, February.
    11. Jin, Fei & Lee, Lung-fei, 2018. "Irregular N2SLS and LASSO estimation of the matrix exponential spatial specification model," Journal of Econometrics, Elsevier, vol. 206(2), pages 336-358.
    12. Tong Tong Wu & Gang Li & Chengyong Tang, 2015. "Empirical Likelihood for Censored Linear Regression and Variable Selection," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 798-812, September.
    13. Ping Zeng & Yongyue Wei & Yang Zhao & Jin Liu & Liya Liu & Ruyang Zhang & Jianwei Gou & Shuiping Huang & Feng Chen, 2014. "Variable selection approach for zero-inflated count data via adaptive lasso," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(4), pages 879-894, April.
    14. Xia, Xiaochao & Liu, Zhi & Yang, Hu, 2016. "Regularized estimation for the least absolute relative error models with a diverging number of covariates," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 104-119.
    15. Hui Xiao & Yiguo Sun, 2019. "On Tuning Parameter Selection in Model Selection and Model Averaging: A Monte Carlo Study," JRFM, MDPI, vol. 12(3), pages 1-16, June.
    16. Zbonakova, L. & Härdle, W.K. & Wang, W., 2016. "Time Varying Quantile Lasso," Working Papers 16/07, Department of Economics, City University London.
    17. Leng, Chenlei & Li, Bo, 2010. "Least squares approximation with a diverging number of parameters," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 254-261, February.
    18. Jianfeng Wei & Jian Yang & Xuewen Cheng & Jie Ding & Shengquan Li, 2023. "Adaptive Regression Analysis of Heterogeneous Data Streams via Models with Dynamic Effects," Mathematics, MDPI, vol. 11(24), pages 1-18, December.
    19. Lee, Eun Ryung & Park, Byeong U., 2012. "Sparse estimation in functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 1-17.
    20. Kaixu Yang & Tapabrata Maiti, 2022. "Ultrahigh‐dimensional generalized additive model: Unified theory and methods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 917-942, September.

    More about this item

    Keywords

    Clustering; Empirical likelihood; Exterior point algorithm; Pairwise mean comparison; Pairwise L1 regularization;
    All these keywords.

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

    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:spr:aistmt:v:73:y:2021:i:1:d:10.1007_s10463-019-00745-z. 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.