IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v103y2016i1p71-88..html
   My bibliography  Save this article

Spatial regression models over two-dimensional manifolds

Author

Listed:
  • B. Ettinger
  • S. Perotto
  • L. M. Sangalli

Abstract

We propose a regression model for data spatially distributed over general two-dimensional Riemannian manifolds. This is a generalized additive model with a roughness penalty term involving a differential operator computed over the non-planar domain. By virtue of a semiparametric framework, the model allows inclusion of space-varying covariate information. Estimation can be performed by conformally parameterizing the non-planar domain and then generalizing existing models for penalized spatial regression over planar domains. The conformal coordinates and the estimation problem are both computed with a finite element approach.

Suggested Citation

  • B. Ettinger & S. Perotto & L. M. Sangalli, 2016. "Spatial regression models over two-dimensional manifolds," Biometrika, Biometrika Trust, vol. 103(1), pages 71-88.
    • Handle: RePEc:oup:biomet:v:103:y:2016:i:1:p:71-88.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asv069
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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. Laura M. Sangalli & Piercesare Secchi & Simone Vantini & Alessandro Veneziani, 2009. "Efficient estimation of three‐dimensional curves and their derivatives by free‐knot regression splines, applied to the analysis of inner carotid artery centrelines," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(3), pages 285-306, July.
    2. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    3. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    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. Laura M. Sangalli, 2021. "Spatial Regression With Partial Differential Equation Regularisation," International Statistical Review, International Statistical Institute, vol. 89(3), pages 505-531, December.
    2. Eleonora Arnone & Luca Negri & Ferruccio Panzica & Laura M. Sangalli, 2023. "Analyzing data in complicated 3D domains: Smoothing, semiparametric regression, and functional principal component analysis," Biometrics, The International Biometric Society, vol. 79(4), pages 3510-3521, December.
    3. Alexander Gleim & Nazarii Salish, 2022. "Forecasting Environmental Data: An example to ground-level ozone concentration surfaces," Papers 2202.03332, arXiv.org.
    4. Arnone, Eleonora & Azzimonti, Laura & Nobile, Fabio & Sangalli, Laura M., 2019. "Modeling spatially dependent functional data via regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 275-295.
    5. Ferraccioli, Federico & Sangalli, Laura M. & Finos, Livio, 2022. "Some first inferential tools for spatial regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    6. Federico Ferraccioli & Eleonora Arnone & Livio Finos & James O. Ramsay & Laura M. Sangalli, 2021. "Nonparametric density estimation over complicated domains," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 346-368, April.
    7. Vieu, Philippe, 2018. "On dimension reduction models for functional data," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 134-138.
    8. Bernardi, Mara S. & Carey, Michelle & Ramsay, James O. & Sangalli, Laura M., 2018. "Modeling spatial anisotropy via regression with partial differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 15-30.

    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. 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".
    2. Dette, Holger & Marchlewski, Mareen, 2007. "A test for the parametric form of the variance function in apartial linear regression model," Technical Reports 2007,26, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Ferraccioli, Federico & Sangalli, Laura M. & Finos, Livio, 2022. "Some first inferential tools for spatial regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    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. Yuejin Zhou & Yebin Cheng & Wenlin Dai & Tiejun Tong, 2018. "Optimal difference-based estimation for partially linear models," Computational Statistics, Springer, vol. 33(2), pages 863-885, June.
    6. Zhu, Xuehu & Wang, Tao & Zhao, Junlong & Zhu, Lixing, 2017. "Inference for biased transformation models," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 105-120.
    7. Kim, Namhyun & W. Saart, Patrick, 2021. "Estimation in partially linear semiparametric models with parametric and/or nonparametric endogeneity," Cardiff Economics Working Papers E2021/9, Cardiff University, Cardiff Business School, Economics Section.
    8. Lu Lin & Lili Liu & Xia Cui & Kangning Wang, 2021. "A generalized semiparametric regression and its efficient estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 1-24, March.
    9. Aifen Feng & Xiaogai Chang & Jingya Fan & Zhengfen Jin, 2023. "Application of LADMM and As-LADMM for a High-Dimensional Partially Linear Model," Mathematics, MDPI, vol. 11(19), pages 1-14, October.
    10. Lian, Heng & Liang, Hua, 2016. "Separation of linear and index covariates in partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 56-70.
    11. Hu Yang & Ning Li & Jing Yang, 2020. "A robust and efficient estimation and variable selection method for partially linear models with large-dimensional covariates," Statistical Papers, Springer, vol. 61(5), pages 1911-1937, October.
    12. Huang, Zhensheng & Pang, Zhen & Hu, Tao, 2013. "Testing structural change in partially linear single-index models with error-prone linear covariates," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 121-133.
    13. Xin Lu & Brent A. Johnson, 2015. "Direct estimation of the mean outcome on treatment when treatment assignment and discontinuation compete," Biometrika, Biometrika Trust, vol. 102(4), pages 797-807.
    14. Zhang, Jun & Feng, Zhenghui & Peng, Heng, 2018. "Estimation and hypothesis test for partial linear multiplicative models," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 87-103.
    15. Wang, Xiuli & Zhao, Shengli & Wang, Mingqiu, 2017. "Restricted profile estimation for partially linear models with large-dimensional covariates," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 71-76.
    16. Graciela Boente & Daniela Rodriguez & Pablo Vena, 2020. "Robust estimators in a generalized partly linear regression model under monotony constraints," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 50-89, March.
    17. Wei Lan & Ronghua Luo & Chih-Ling Tsai & Hansheng Wang & Yunhong Yang, 2015. "Testing the Diagonality of a Large Covariance Matrix in a Regression Setting," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 76-86, January.
    18. Q. Shao, 2009. "Seasonality analysis of time series in partial linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(7), pages 827-837.
    19. M. Arashi & Mahdi Roozbeh, 2019. "Some improved estimation strategies in high-dimensional semiparametric regression models with application to riboflavin production data," Statistical Papers, Springer, vol. 60(3), pages 667-686, June.
    20. Yixin Fang & Heng Lian & Hua Liang, 2018. "A generalized partially linear framework for variance functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 1147-1175, October.

    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:oup:biomet:v:103:y:2016:i:1:p:71-88.. 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.