IDEAS home Printed from https://ideas.repec.org/a/eee/ecosta/v14y2020icp89-111.html
   My bibliography  Save this article

Regression with I-priors

Author

Listed:
  • Bergsma, Wicher P

Abstract

The problem of estimating a parametric or nonparametric regression function in a model with normal errors is considered. For this purpose, a novel objective prior for the regression function is proposed, defined as the distribution maximizing entropy subject to a suitable constraint based on the Fisher information on the regression function. The prior is named I-prior. For the present model, it is Gaussian with covariance kernel proportional to the Fisher information, and mean chosen a priori (e.g., 0).

Suggested Citation

  • Bergsma, Wicher P, 2020. "Regression with I-priors," Econometrics and Statistics, Elsevier, vol. 14(C), pages 89-111.
    • Handle: RePEc:eee:ecosta:v:14:y:2020:i:c:p:89-111
    DOI: 10.1016/j.ecosta.2019.10.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2452306219300632
    Download Restriction: Full text for ScienceDirect subscribers only. Contains open access articles
    File URL: https://libkey.io/10.1016/j.ecosta.2019.10.002?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. Hongxiao Zhu & Fang Yao & Hao Helen Zhang, 2014. "Structured functional additive regression in reproducing kernel Hilbert spaces," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 581-603, June.
    2. Timothy I. Cannings & Richard J. Samworth, 2017. "Random-projection ensemble classification," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 959-1035, September.
    3. Lian, Heng & Li, Gaorong, 2014. "Series expansion for functional sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 150-165.
    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. Bergsma, Wicher, 2020. "Regression with I-priors," LSE Research Online Documents on Economics 102136, London School of Economics and Political Science, LSE Library.
    2. Huang, Lele & Zhao, Junlong & Wang, Huiwen & Wang, Siyang, 2016. "Robust shrinkage estimation and selection for functional multiple linear model through LAD loss," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 384-400.
    3. Lili Xia & Tingyu Lai & Zhongzhan Zhang, 2023. "An Adaptive-to-Model Test for Parametric Functional Single-Index Model," Mathematics, MDPI, vol. 11(8), pages 1-25, April.
    4. Allam, Abdelaziz & Mourid, Tahar, 2019. "Optimal rate for covariance operator estimators of functional autoregressive processes with random coefficients," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 130-137.
    5. Yu-Ru Su & Chong-Zhi Di & Li Hsu, 2017. "Hypothesis testing in functional linear models," Biometrics, The International Biometric Society, vol. 73(2), pages 551-561, June.
    6. Fuli Zhang & Kung‐Sik Chan, 2023. "Random projection ensemble classification with high‐dimensional time series," Biometrics, The International Biometric Society, vol. 79(2), pages 964-974, June.
    7. Yuping Hu & Siyu Wu & Sanying Feng & Junliang Jin, 2020. "Estimation in Partial Functional Linear Spatial Autoregressive Model," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
    8. Guochang Wang & Jianjun Zhou & Wuqing Wu & Min Chen, 2017. "Robust functional sliced inverse regression," Statistical Papers, Springer, vol. 58(1), pages 227-245, March.
    9. Jiang, Qing & Hušková, Marie & Meintanis, Simos G. & Zhu, Lixing, 2019. "Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 202-220.
    10. Zardad Khan & Asma Gul & Aris Perperoglou & Miftahuddin Miftahuddin & Osama Mahmoud & Werner Adler & Berthold Lausen, 2020. "Ensemble of optimal trees, random forest and random projection ensemble classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(1), pages 97-116, March.
    11. Guochang Wang & Xiang-Nan Feng & Min Chen, 2016. "Functional Partial Linear Single-index Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 261-274, March.
    12. Kehui Chen & Xiaoke Zhang & Alexander Petersen & Hans-Georg Müller, 2017. "Quantifying Infinite-Dimensional Data: Functional Data Analysis in Action," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 582-604, December.
    13. Xu, Jianjun & Cui, Wenquan, 2022. "A new RKHS-based global testing for functional linear model," Statistics & Probability Letters, Elsevier, vol. 182(C).
    14. Maeng, Hye Young & Fryzlewicz, Piotr, 2019. "Regularised forecasting via smooth-rough partitioning of the regression coefficients," LSE Research Online Documents on Economics 100878, London School of Economics and Political Science, LSE Library.
    15. Deepak Nag Ayyala & Santu Ghosh & Daniel F. Linder, 2022. "Covariance matrix testing in high dimension using random projections," Computational Statistics, Springer, vol. 37(3), pages 1111-1141, July.
    16. Jingjing Yang & Dennis D. Cox & Jong Soo Lee & Peng Ren & Taeryon Choi, 2017. "Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian–Wishart processes," Biometrics, The International Biometric Society, vol. 73(4), pages 1082-1091, December.
    17. Wong, Raymond K.W. & Zhang, Xiaoke, 2019. "Nonparametric operator-regularized covariance function estimation for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 131-144.
    18. Liu, Yuzi & Peng, Ling & Liu, Qing & Lian, Heng & Liu, Xiaohui, 2023. "Functional additive expectile regression in the reproducing kernel Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    19. Lin, Hongmei & Jiang, Xuejun & Lian, Heng & Zhang, Weiping, 2019. "Reduced rank modeling for functional regression with functional responses," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 205-217.
    20. Philip T. Reiss & Jeff Goldsmith & Han Lin Shang & R. Todd Ogden, 2017. "Methods for Scalar-on-Function Regression," International Statistical Review, International Statistical Institute, vol. 85(2), pages 228-249, August.

    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:ecosta:v:14:y:2020:i:c:p:89-111. 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: https://www.journals.elsevier.com/econometrics-and-statistics .

    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.