IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v162y2021ics0167947321000992.html
   My bibliography  Save this article

Distributed one-step upgraded estimation for non-uniformly and non-randomly distributed data

Author

Listed:
  • Wang, Feifei
  • Zhu, Yingqiu
  • Huang, Danyang
  • Qi, Haobo
  • Wang, Hansheng

Abstract

One-shot-type (or divide-and-conquer) estimators have been widely used for distributed statistical analysis. However, their outstanding statistical efficiency hinges on two critical conditions. The first is the uniformity condition, which requires that the sample sizes allocated to different Workers should be as comparable as possible. The second one is the randomness condition, which requires that the data should be distributed across Workers as randomly as possible. Both conditions are often violated in practice. The violation of either condition can be seriously degrade the statistical efficiency of one-shot estimators, or even make them inconsistent. To fix this problem, a novel one-step upgraded pilot (OSUP) method is proposed. In the first step of the algorithm, a pilot estimate is computed based on randomly selected samples from different Workers. In the second step, one-step updating is conducted based on the pilot estimate by summarizing the derivative information on each Worker. The resulting OSUP estimator is theoretically proved to be as statistically efficient as the whole sample maximum likelihood estimator without any restrictive assumption about distribution uniformity and randomness. Extensive numerical studies are presented to demonstrate the finite sample performance of the OSUP estimator. Finally, by way of an illustration, an American Airlines dataset is analyzed on a Spark cluster.

Suggested Citation

  • Wang, Feifei & Zhu, Yingqiu & Huang, Danyang & Qi, Haobo & Wang, Hansheng, 2021. "Distributed one-step upgraded estimation for non-uniformly and non-randomly distributed data," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:csdana:v:162:y:2021:i:c:s0167947321000992
    DOI: 10.1016/j.csda.2021.107265
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947321000992
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2021.107265?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. Lam, Clifford & Fan, Jianqing, 2008. "Profile-kernel likelihood inference with diverging number of parameters," LSE Research Online Documents on Economics 31548, London School of Economics and Political Science, LSE Library.
    2. 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.
    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. Wu, Shihao & Li, Zhe & Zhu, Xuening, 2023. "A distributed community detection algorithm for large scale networks under stochastic block models," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).

    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. Fan, Guo-Liang & Liang, Han-Ying & Shen, Yu, 2016. "Penalized empirical likelihood for high-dimensional partially linear varying coefficient model with measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 183-201.
    2. Li, Degui & Linton, Oliver & Lu, Zudi, 2015. "A flexible semiparametric forecasting model for time series," Journal of Econometrics, Elsevier, vol. 187(1), pages 345-357.
    3. Lv, Zhike & Zhu, Huiming & Yu, Keming, 2014. "Robust variable selection for nonlinear models with diverging number of parameters," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 90-97.
    4. Xia Cui & Heng Peng & Songqiao Wen & Lixing Zhu, 2013. "Component Selection in the Additive Regression Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 491-510, September.
    5. Zhaoping Hong & Yuao Hu & Heng Lian, 2013. "Variable selection for high-dimensional varying coefficient partially linear models via nonconcave penalty," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(7), pages 887-908, October.
    6. Qian, Junhui & Su, Liangjun, 2016. "Shrinkage estimation of common breaks in panel data models via adaptive group fused Lasso," Journal of Econometrics, Elsevier, vol. 191(1), pages 86-109.
    7. Lu, Xun & Su, Liangjun, 2016. "Shrinkage estimation of dynamic panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 190(1), pages 148-175.
    8. Lichun Wang & Peng Lai & Heng Lian, 2013. "Polynomial spline estimation for generalized varying coefficient partially linear models with a diverging number of components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(8), pages 1083-1103, November.
    9. Weihua Zhao & Riquan Zhang & Jicai Liu & Yazhao Lv, 2014. "Robust and efficient variable selection for semiparametric partially linear varying coefficient model based on modal regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 165-191, February.
    10. Degui Li & Jia Chen & Zhengyan Lin, 2009. "Variable selection in partially time-varying coefficient models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(5), pages 553-566.
    11. Byeong U. Park & Enno Mammen & Young K. Lee & Eun Ryung Lee, 2015. "Varying Coefficient Regression Models: A Review and New Developments," International Statistical Review, International Statistical Institute, vol. 83(1), pages 36-64, April.
    12. Shen, Yu & Liang, Han-Ying, 2018. "Quantile regression for partially linear varying-coefficient model with censoring indicators missing at random," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 1-18.
    13. Lee, Sangin & Kim, Yongdai & Kwon, Sunghoon, 2012. "Quadratic approximation for nonconvex penalized estimations with a diverging number of parameters," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1710-1717.
    14. Lian, Heng & Meng, Jie & Zhao, Kaifeng, 2015. "Spline estimator for simultaneous variable selection and constant coefficient identification in high-dimensional generalized varying-coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 81-103.
    15. Degao Li & Guodong Li & Jinhong You, 2014. "Significant Variable Selection And Autoregressive Order Determination For Time-Series Partially Linear Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 478-490, August.
    16. 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.
    17. 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.
    18. Guan, Wei & Gray, Alexander, 2013. "Sparse high-dimensional fractional-norm support vector machine via DC programming," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 136-148.
    19. Margherita Giuzio, 2017. "Genetic algorithm versus classical methods in sparse index tracking," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 243-256, November.
    20. Chang, Jinyuan & Chen, Song Xi & Chen, Xiaohong, 2015. "High dimensional generalized empirical likelihood for moment restrictions with dependent data," Journal of Econometrics, Elsevier, vol. 185(1), pages 283-304.

    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:162:y:2021:i:c:s0167947321000992. 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.