IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v71y2019i4d10.1007_s10463-018-0661-1.html
   My bibliography  Save this article

Robust functional estimation in the multivariate partial linear model

Author

Listed:
  • Michael Levine

    (Purdue University)

Abstract

We consider the problem of adaptive estimation of the functional component in a partial linear model where the argument of the function is defined on a q-dimensional grid. Obtaining an adaptive estimator of this functional component is an important practical problem in econometrics where exact distributions of random errors and the parametric component are mostly unknown. An estimator of the functional component that is adaptive over the wide range of multivariate Besov classes and robust to a wide choice of distributions of the linear component and random errors is constructed. It is also shown that the same estimator is locally adaptive over the same range of Besov classes and robust over large collections of distributions of the linear component and random errors as well. At any fixed point, this estimator attains a local adaptive minimax rate.

Suggested Citation

  • Michael Levine, 2019. "Robust functional estimation in the multivariate partial linear model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 743-770, August.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:4:d:10.1007_s10463-018-0661-1
    DOI: 10.1007/s10463-018-0661-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-018-0661-1
    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/s10463-018-0661-1?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. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    2. Chuanhua Wei & Xiaonan Wang, 2016. "Liu-type estimator in semiparametric partially linear additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(3), pages 459-468, September.
    3. Schick, Anton, 1996. "Root-n consistent estimation in partly linear regression models," Statistics & Probability Letters, Elsevier, vol. 28(4), pages 353-358, August.
    4. Marianna Pensky & Brani Vidakovic, 2001. "On Non-Equally Spaced Wavelet Regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 681-690, December.
    5. Zhang, Shuanglin & Wong, Man-Yu & Zheng, Zhongguo, 2002. "Wavelet Threshold Estimation of a Regression Function with Random Design," Journal of Multivariate Analysis, Elsevier, vol. 80(2), pages 256-284, February.
    6. He, Xuming & Shi, Peide, 1996. "Bivariate Tensor-Product B-Splines in a Partly Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 162-181, August.
    7. Antoniadis, Anestis & Dinh Tuan Pham, 1998. "Wavelet regression for random or irregular design," Computational Statistics & Data Analysis, Elsevier, vol. 28(4), pages 353-369, October.
    8. Levine, Michael, 2015. "Minimax rate of convergence for an estimator of the functional component in a semiparametric multivariate partially linear model," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 283-290.
    9. Richard Schmalensee & Thomas M. Stoker, 1999. "Household Gasoline Demand in the United States," Econometrica, Econometric Society, vol. 67(3), pages 645-662, May.
    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. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    2. Kim, Kun Ho & Chao, Shih-Kang & Härdle, Wolfgang Karl, 2020. "Simultaneous Inference of the Partially Linear Model with a Multivariate Unknown Function," IRTG 1792 Discussion Papers 2020-008, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    3. Horowitz, Joel L. & Lee, Sokbae, 2005. "Nonparametric Estimation of an Additive Quantile Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1238-1249, December.
    4. Cui, Xia & Lu, Ying & Peng, Heng, 2017. "Estimation of partially linear regression models under the partial consistency property," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 103-121.
    5. Fujii, Toru & Konishi, Sadanori, 2006. "Nonlinear regression modeling via regularized wavelets and smoothing parameter selection," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 2023-2033, October.
    6. Han Shang, 2014. "Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density," Computational Statistics, Springer, vol. 29(3), pages 829-848, June.
    7. Haotian Chen & Xibin Zhang, 2014. "Bayesian Estimation for Partially Linear Models with an Application to Household Gasoline Consumption," Monash Econometrics and Business Statistics Working Papers 28/14, Monash University, Department of Econometrics and Business Statistics.
    8. Chen, Haotian & Smyth, Russell & Zhang, Xibin, 2017. "A Bayesian sampling approach to measuring the price responsiveness of gasoline demand using a constrained partially linear model," Energy Economics, Elsevier, vol. 67(C), pages 346-354.
    9. Manzan, sebastiano & Zerom, Dawit, 2008. "A Semiparametric Analysis of Gasoline Demand in the US: Reexamining The Impact of Price," MPRA Paper 14386, University Library of Munich, Germany.
    10. Leandro De Magalhães & Lucas Ferrero, 2012. "Separation of Powers and the Size of Government in the U.S. States," The Centre for Market and Public Organisation 12/285, The Centre for Market and Public Organisation, University of Bristol, UK.
    11. Ibacache-Pulgar, Germán & Paula, Gilberto A., 2011. "Local influence for Student-t partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1462-1478, March.
    12. Leandro De Magalhães & Lucas Ferrero, 2015. "Separation of powers and the tax level in the U.S. states," Southern Economic Journal, John Wiley & Sons, vol. 82(2), pages 598-619, October.
    13. Liang, Hua & Härdle, Wolfgang, 1997. "Large sample theory of the estimation of the error distribution for a semiparametric model," SFB 373 Discussion Papers 1997,101, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    14. Jean‐Pierre Florens & Jan Johannes & Sébastien Van Bellegem, 2012. "Instrumental regression in partially linear models," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 304-324, June.
    15. Wang, Qihua & Sun, Zhihua, 2007. "Estimation in partially linear models with missing responses at random," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1470-1493, August.
    16. Cai, Zongwu & Xiao, Zhijie, 2012. "Semiparametric quantile regression estimation in dynamic models with partially varying coefficients," Journal of Econometrics, Elsevier, vol. 167(2), pages 413-425.
    17. Sebastiano Manzan & Dawit Zerom, 2010. "A Semiparametric Analysis of Gasoline Demand in the United States Reexamining The Impact of Price," Econometric Reviews, Taylor & Francis Journals, vol. 29(4), pages 439-468.
    18. repec:wyi:journl:002114 is not listed on IDEAS
    19. Chen, Qihui, 2021. "Robust and optimal estimation for partially linear instrumental variables models with partial identification," Journal of Econometrics, Elsevier, vol. 221(2), pages 368-380.
    20. Liang, Hua, 2006. "Estimation in partially linear models and numerical comparisons," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 675-687, February.
    21. repec:spo:wpmain:info:hdl:2441/7182 is not listed on IDEAS
    22. Kyle Colangelo & Ying-Ying Lee, 2019. "Double debiased machine learning nonparametric inference with continuous treatments," CeMMAP working papers CWP72/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    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:71:y:2019:i:4:d:10.1007_s10463-018-0661-1. 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.