IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v192y2024ics0167947323002025.html
   My bibliography  Save this article

Simultaneous confidence region of an embedded one-dimensional curve in multi-dimensional space

Author

Listed:
  • Yamazoe, Hiroya
  • Naito, Kanta

Abstract

This paper focuses on the simultaneous confidence region of a one-dimensional curve embedded in multi-dimensional space. Local linear regression is applied component-wise to each variable in multi-dimensional data, which yields an estimator of the one-dimensional curve. A simultaneous confidence region of the curve is proposed based on this estimator and theoretical results for the estimator and the region are developed under some reasonable assumptions. Practically efficient algorithms to determine the thickness of the region are also addressed. The effectiveness of the region is investigated through simulation studies and applications to artificial and real datasets, which reveal that the proposed simultaneous confidence region works well.

Suggested Citation

  • Yamazoe, Hiroya & Naito, Kanta, 2024. "Simultaneous confidence region of an embedded one-dimensional curve in multi-dimensional space," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:csdana:v:192:y:2024:i:c:s0167947323002025
    DOI: 10.1016/j.csda.2023.107891
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947323002025
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2023.107891?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. Liu, Yang & Ruppert, David, 2021. "Density estimation on a network," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    2. Adrian Baddeley & Aruna Jammalamadaka & Gopalan Nair, 2014. "Multitype point process analysis of spines on the dendrite network of a neuron," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(5), pages 673-694, November.
    3. Greg McSwiggan & Adrian Baddeley & Gopalan Nair, 2017. "Kernel Density Estimation on a Linear Network," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 324-345, June.
    4. Harman, Radoslav & Lacko, Vladimír, 2010. "On decompositional algorithms for uniform sampling from n-spheres and n-balls," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2297-2304, November.
    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. Liu, Yang & Ruppert, David, 2021. "Density estimation on a network," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    2. Matthias Eckardt & Jorge Mateu, 2021. "Second-order and local characteristics of network intensity functions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 318-340, June.
    3. Wolf-Dieter Richter, 2019. "On (p1,…,pk)-spherical distributions," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-18, December.
    4. Kristian Bjørn Hessellund & Ganggang Xu & Yongtao Guan & Rasmus Waagepetersen, 2022. "Second‐order semi‐parametric inference for multivariate log Gaussian Cox processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(1), pages 244-268, January.
    5. Jakob G. Rasmussen & Heidi S. Christensen, 2021. "Point Processes on Directed Linear Networks," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 647-667, June.
    6. Abadir, Karim M. & Luati, Alessandra & Paruolo, Paolo, 2023. "GARCH density and functional forecasts," Journal of Econometrics, Elsevier, vol. 235(2), pages 470-483.
    7. Guillaume Grégoire & Josée Fortin & Isa Ebtehaj & Hossein Bonakdari, 2022. "Novel Hybrid Statistical Learning Framework Coupled with Random Forest and Grasshopper Optimization Algorithm to Forecast Pesticide Use on Golf Courses," Agriculture, MDPI, vol. 12(7), pages 1-19, June.
    8. Filippozzi, Rafaela & Gonçalves, Douglas S. & Santos, Luiz-Rafael, 2023. "First-order methods for the convex hull membership problem," European Journal of Operational Research, Elsevier, vol. 306(1), pages 17-33.
    9. Alexandru Agapie, 2021. "Spherical Distributions Used in Evolutionary Algorithms," Mathematics, MDPI, vol. 9(23), pages 1-15, November.
    10. Laura Anton-Sanchez & Pedro Larrañaga & Ruth Benavides-Piccione & Isabel Fernaud-Espinosa & Javier DeFelipe & Concha Bielza, 2017. "Three-dimensional spatial modeling of spines along dendritic networks in human cortical pyramidal neurons," PLOS ONE, Public Library of Science, vol. 12(6), pages 1-14, June.
    11. Jean-Thomas Camino & Christian Artigues & Laurent Houssin & Stéphane Mourgues, 2019. "Linearization of Euclidean norm dependent inequalities applied to multibeam satellites design," Computational Optimization and Applications, Springer, vol. 73(2), pages 679-705, June.
    12. Arnone, Eleonora & Ferraccioli, Federico & Pigolotti, Clara & Sangalli, Laura M., 2022. "A roughness penalty approach to estimate densities over two-dimensional manifolds," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    13. Nicoletta D’Angelo & Giada Adelfio & Jorge Mateu, 2023. "Local inhomogeneous second-order characteristics for spatio-temporal point processes occurring on linear networks," Statistical Papers, Springer, vol. 64(3), pages 779-805, June.
    14. Greg McSwiggan & Adrian Baddeley & Gopalan Nair, 2017. "Kernel Density Estimation on a Linear Network," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 324-345, June.
    15. Vic Patrangenaru & Peter Bubenik & Robert L. Paige & Daniel Osborne, 2019. "Challenges in Topological Object Data Analysis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 244-271, February.
    16. Vladimír Lacko & Radoslav Harman, 2012. "A conditional distribution approach to uniform sampling on spheres and balls in L p spaces," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(7), pages 939-951, October.
    17. 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.

    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:csdana:v:192:y:2024:i:c:s0167947323002025. 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: http://www.elsevier.com/locate/csda .

    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.