IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/102111.html
   My bibliography  Save this paper

A massive data framework for M-estimators with cubic-rate

Author

Listed:
  • Shi, Chengchun
  • Lu, Wenbin
  • Song, Rui

Abstract

The divide and conquer method is a common strategy for handling massive data. In this article, we study the divide and conquer method for cubic-rate estimators under the massive data framework. We develop a general theory for establishing the asymptotic distribution of the aggregated M-estimators using a weighted average with weights depending on the subgroup sample sizes. Under certain condition on the growing rate of the number of subgroups, the resulting aggregated estimators are shown to have faster convergence rate and asymptotic normal distribution, which are more tractable in both computation and inference than the original M-estimators based on pooled data. Our theory applies to a wide class of M-estimators with cube root convergence rate, including the location estimator, maximum score estimator, and value search estimator. Empirical performance via simulations and a real data application also validate our theoretical findings. Supplementary materials for this article are available online.

Suggested Citation

  • Shi, Chengchun & Lu, Wenbin & Song, Rui, 2018. "A massive data framework for M-estimators with cubic-rate," LSE Research Online Documents on Economics 102111, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:102111
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/102111/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Baqun Zhang & Anastasios A. Tsiatis & Eric B. Laber & Marie Davidian, 2012. "A Robust Method for Estimating Optimal Treatment Regimes," Biometrics, The International Biometric Society, vol. 68(4), pages 1010-1018, December.
    2. Ariel Kleiner & Ameet Talwalkar & Purnamrita Sarkar & Michael I. Jordan, 2014. "A scalable bootstrap for massive data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(4), pages 795-816, September.
    3. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
    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. Fengrui Di & Lei Wang, 2022. "Multi-round smoothed composite quantile regression for distributed data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(5), pages 869-893, October.
    2. Zhang, Haixiang & Wang, HaiYing, 2021. "Distributed subdata selection for big data via sampling-based approach," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    3. Xuejun Ma & Shaochen Wang & Wang Zhou, 2022. "Statistical inference in massive datasets by empirical likelihood," Computational Statistics, Springer, vol. 37(3), pages 1143-1164, July.
    4. 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).
    5. Shi, Jianwei & Qin, Guoyou & Zhu, Huichen & Zhu, Zhongyi, 2021. "Communication-efficient distributed M-estimation with missing data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    6. Zhao, Yan-Yong & Zhang, Yuchun & Liu, Yuan & Ismail, Noriszura, 2024. "Distributed debiased estimation of high-dimensional partially linear models with jumps," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    7. Lulu Zuo & Haixiang Zhang & HaiYing Wang & Liuquan Sun, 2021. "Optimal subsample selection for massive logistic regression with distributed data," Computational Statistics, Springer, vol. 36(4), pages 2535-2562, December.
    8. Le-Yu Chen & Sokbae Lee, 2018. "High Dimensional Classification through $\ell_0$-Penalized Empirical Risk Minimization," Papers 1811.09540, arXiv.org.
    9. Tom Boot & Art=uras Juodis, 2023. "Uniform Inference in Linear Error-in-Variables Models: Divide-and-Conquer," Papers 2301.04439, arXiv.org.
    10. Ma, Xuejun & Wang, Shaochen & Zhou, Wang, 2021. "Testing multivariate quantile by empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 182(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. Xingcai Zhou & Zhaoyang Jing & Chao Huang, 2024. "Distributed Bootstrap Simultaneous Inference for High-Dimensional Quantile Regression," Mathematics, MDPI, vol. 12(5), pages 1-54, February.
    2. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2013. "Testing Many Moment Inequalities," CeMMAP working papers 65/13, Institute for Fiscal Studies.
    3. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Q. Clairon & R. Henderson & N. J. Young & E. D. Wilson & C. J. Taylor, 2021. "Adaptive treatment and robust control," Biometrics, The International Biometric Society, vol. 77(1), pages 223-236, March.
    5. repec:hum:wpaper:sfb649dp2015-031 is not listed on IDEAS
    6. repec:hum:wpaper:sfb649dp2014-067 is not listed on IDEAS
    7. Michael C Knaus & Michael Lechner & Anthony Strittmatter, 2021. "Machine learning estimation of heterogeneous causal effects: Empirical Monte Carlo evidence," The Econometrics Journal, Royal Economic Society, vol. 24(1), pages 134-161.
    8. Shengchun Kong & Zhuqing Yu & Xianyang Zhang & Guang Cheng, 2021. "High‐dimensional robust inference for Cox regression models using desparsified Lasso," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 1068-1095, September.
    9. Magne Mogstad & Joseph P Romano & Azeem M Shaikh & Daniel Wilhelm, 2024. "Inference for Ranks with Applications to Mobility across Neighbourhoods and Academic Achievement across Countries," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(1), pages 476-518.
    10. Xin Qiu & Donglin Zeng & Yuanjia Wang, 2018. "Estimation and evaluation of linear individualized treatment rules to guarantee performance," Biometrics, The International Biometric Society, vol. 74(2), pages 517-528, June.
    11. Brice Ozenne & Esben Budtz-Jørgensen & Sebastian Elgaard Ebert, 2023. "Controlling the familywise error rate when performing multiple comparisons in a linear latent variable model," Computational Statistics, Springer, vol. 38(1), pages 1-23, March.
    12. Crystal T. Nguyen & Daniel J. Luckett & Anna R. Kahkoska & Grace E. Shearrer & Donna Spruijt‐Metz & Jaimie N. Davis & Michael R. Kosorok, 2020. "Estimating individualized treatment regimes from crossover designs," Biometrics, The International Biometric Society, vol. 76(3), pages 778-788, September.
    13. Ruoqing Zhu & Ying-Qi Zhao & Guanhua Chen & Shuangge Ma & Hongyu Zhao, 2017. "Greedy outcome weighted tree learning of optimal personalized treatment rules," Biometrics, The International Biometric Society, vol. 73(2), pages 391-400, June.
    14. Hansen, Christian & Liao, Yuan, 2019. "The Factor-Lasso And K-Step Bootstrap Approach For Inference In High-Dimensional Economic Applications," Econometric Theory, Cambridge University Press, vol. 35(3), pages 465-509, June.
    15. Alexandre Belloni & Victor Chernozhukov & Kengo Kato, 2013. "Uniform post selection inference for LAD regression and other z-estimation problems," CeMMAP working papers CWP74/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Alexandre Belloni & Victor Chernozhukov & Abhishek Kaul, 2017. "Confidence bands for coefficients in high dimensional linear models with error-in-variables," CeMMAP working papers CWP22/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    17. Guangbao Guo & Yue Sun & Xuejun Jiang, 2020. "A partitioned quasi-likelihood for distributed statistical inference," Computational Statistics, Springer, vol. 35(4), pages 1577-1596, December.
    18. Giovanni Cerulli, 2020. "Optimal Policy Learning: From Theory to Practice," Papers 2011.04993, arXiv.org.
    19. Yuta Koike, 2023. "High-Dimensional Central Limit Theorems for Homogeneous Sums," Journal of Theoretical Probability, Springer, vol. 36(1), pages 1-45, March.
    20. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney K. Newey, 2016. "Double machine learning for treatment and causal parameters," CeMMAP working papers 49/16, Institute for Fiscal Studies.
    21. Wu Wang & Xuming He & Zhongyi Zhu, 2020. "Statistical inference for multiple change‐point models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1149-1170, December.
    22. Philipp Bach & Victor Chernozhukov & Malte S. Kurz & Martin Spindler & Sven Klaassen, 2021. "DoubleML -- An Object-Oriented Implementation of Double Machine Learning in R," Papers 2103.09603, arXiv.org, revised Jun 2024.

    More about this item

    Keywords

    cubic rate asymptotics; divide and conquer; M-estimators; massive data;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ehl:lserod:102111. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    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.