IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v61y1999i4p927-943.html

One‐step local quasi‐likelihood estimation

Author

Listed:
  • J. Fan
  • J. Chen

Abstract

Local quasi‐likelihood estimation is a useful extension of local least squares methods, but its computational cost and algorithmic convergence problems make the procedure less appealing, particularly when it is iteratively used in methods such as the back‐fitting algorithm, cross‐validation and bootstrapping. A one‐step local quasi‐likelihood estimator is introduced to overcome the computational drawbacks of the local quasi‐likelihood method. We demonstrate that as long as the initial estimators are reasonably good, the one‐step estimator has the same asymptotic behaviour as the local quasi‐likelihood method. Our simulation shows that the one‐step estimator performs at least as well as the local quasi‐likelihood method for a wide range of choices of bandwidths. A data‐driven bandwidth selector is proposed for the one‐step estimator based on the pre‐asymptotic substitution method of Fan and Gijbels. It is then demonstrated that the data‐driven one‐step local quasi‐likelihood estimator performs as well as the maximum local quasi‐likelihood estimator by using the ideal optimal bandwidth.

Suggested Citation

  • J. Fan & J. Chen, 1999. "One‐step local quasi‐likelihood estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 927-943.
    • Handle: RePEc:bla:jorssb:v:61:y:1999:i:4:p:927-943
    DOI: 10.1111/1467-9868.00211
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9868.00211
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9868.00211?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Robert Bassett & Julio Deride, 2022. "One-Step Estimation with Scaled Proximal Methods," Mathematics of Operations Research, INFORMS, vol. 47(3), pages 2366-2386, August.
    2. Chunming Zhang, 2008. "Prediction Error Estimation Under Bregman Divergence for Non‐Parametric Regression and Classification," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 496-523, September.
    3. Jing Wang & Lijian Yang, 2009. "Efficient and fast spline-backfitted kernel smoothing of additive models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 663-690, September.
    4. Minggen Lu, 2017. "Efficient estimation of quasi-likelihood models using B-splines," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 1099-1127, October.
    5. repec:cam:camjip:2206 is not listed on IDEAS
    6. Talamakrouni, Majda & El Ghouch, Anouar & Van Keilegom, Ingrid, 2016. "Parametrically guided local quasi-likelihood with censored data," LIDAM Discussion Papers ISBA 2016011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Shangyu Xie & Yong Zhou & Alan T. K. Wan, 2014. "A Varying-Coefficient Expectile Model for Estimating Value at Risk," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 576-592, October.
    8. Linke, Yu.Yu. & Borisov, I.S., 2017. "Constructing initial estimators in one-step estimation procedures of nonlinear regression," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 87-94.
    9. Jianwen Cai & Jianqing Fan & Jiancheng Jiang & Haibo Zhou, 2008. "Partially linear hazard regression with varying coefficients for multivariate survival data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 141-158, February.
    10. Chen, Jia & Li, Degui & Zhang, Lixin, 2010. "Robust estimation in a nonlinear cointegration model," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 706-717, March.
    11. Zhao, Yan-Yong & Lin, Jin-Guan & Xu, Pei-Rong & Ye, Xu-Guo, 2015. "Orthogonality-projection-based estimation for semi-varying coefficient models with heteroscedastic errors," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 204-221.
    12. Zhao, Xiaobing & Zhou, Xian, 2012. "Estimation of medical costs by copula models with dynamic change of health status," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 480-491.
    13. Linke, Yuliana Yu., 2017. "Asymptotic normality of one-step M-estimators based on non-identically distributed observations," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 216-221.
    14. Karunamuni, Rohana J. & Wu, Jingjing, 2011. "One-step minimum Hellinger distance estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3148-3164, December.
    15. Jih-Chang Yu & Yu-Jen Cheng, 2025. "Estimation and variable selection for semiparametric transformation models with length-biased survival data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 31(3), pages 674-701, July.
    16. Zhao, Xiaobing & Zhou, Xian, 2012. "Modeling gap times between recurrent events by marginal rate function," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 370-383.
    17. Hafner, Christian & Linton, Oliver & Wang, Linqi, 2022. "Dynamic Autoregressive Liquidity (DArLiQ)," LIDAM Discussion Papers ISBA 2022009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    18. Masao Ueki & Kaoru Fueda, 2010. "Boosting local quasi-likelihood estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(2), pages 235-248, April.

    More about this item

    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:bla:jorssb:v:61:y:1999:i:4:p:927-943. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.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.