IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v121y2013icp152-175.html
   My bibliography  Save this article

Kernel density estimation for directional–linear data

Author

Listed:
  • García-Portugués, Eduardo
  • Crujeiras, Rosa M.
  • González-Manteiga, Wenceslao

Abstract

A nonparametric kernel density estimator for directional–linear data is introduced. The proposal is based on a product kernel accounting for the different nature of both (directional and linear) components of the random vector. Expressions for the bias, variance, and mean integrated square error (MISE) are derived, jointly with an asymptotic normality result for the proposed estimator. For some particular distributions, an explicit formula for the MISE is obtained and compared with its asymptotic version, both for directional and directional–linear kernel density estimators. In this same setting, a closed expression for the bootstrap MISE is also derived.

Suggested Citation

  • García-Portugués, Eduardo & Crujeiras, Rosa M. & González-Manteiga, Wenceslao, 2013. "Kernel density estimation for directional–linear data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 152-175.
  • Handle: RePEc:eee:jmvana:v:121:y:2013:i:c:p:152-175
    DOI: 10.1016/j.jmva.2013.06.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X13001309
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jmva.2013.06.009?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. Pelletier, Bruno, 2005. "Kernel density estimation on Riemannian manifolds," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 297-304, July.
    2. Oliveira, M. & Crujeiras, R.M. & Rodríguez-Casal, A., 2012. "A plug-in rule for bandwidth selection in circular density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3898-3908.
    3. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
    4. Cao, R., 1993. "Bootstrapping the Mean Integrated Squared Error," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 137-160, April.
    5. Bai, Z. D. & Rao, C. Radhakrishna & Zhao, L. C., 1988. "Kernel estimators of density function of directional data," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 24-39, October.
    6. Taylor, Charles C., 2008. "Automatic bandwidth selection for circular density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3493-3500, March.
    7. Cao, Ricardo & Cuevas, Antonio & Gonzalez Manteiga, Wensceslao, 1994. "A comparative study of several smoothing methods in density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 17(2), pages 153-176, February.
    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. Fernández-de-Marcos, Alberto & García-Portugués, Eduardo, 2023. "Data-driven stabilizations of goodness-of-fit tests," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    2. Jeon, Jeong Min & Van Keilegom, Ingrid, 2023. "Density estimation for mixed Euclidean and non-Euclidean data in the presence of measurement error," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    3. Di Marzio, Marco & Fensore, Stefania & Panzera, Agnese & Taylor, Charles C., 2019. "Kernel density classification for spherical data," Statistics & Probability Letters, Elsevier, vol. 144(C), pages 23-29.
    4. Andrea Meilán-Vila & Mario Francisco-Fernández & Rosa M. Crujeiras & Agnese Panzera, 2021. "Nonparametric multiple regression estimation for circular response," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 650-672, September.
    5. Paula Saavedra-Nieves & Rosa M. Crujeiras, 2022. "Nonparametric estimation of directional highest density regions," 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. 16(3), pages 761-796, September.
    6. Aboubacar Amiri & Baba Thiam & Thomas Verdebout, 2017. "On the Estimation of the Density of a Directional Data Stream," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 249-267, March.
    7. Zihao Wu & Carolina Euan & Rosa M. Crujeiras & Ying Sun, 2023. "Estimation and Clustering of Directional Wave Spectra," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(3), pages 502-525, September.
    8. Eduardo García‐Portugués & Javier Álvarez‐Liébana & Gonzalo Álvarez‐Pérez & Wenceslao González‐Manteiga, 2021. "A goodness‐of‐fit test for the functional linear model with functional response," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 502-528, June.
    9. Fernández de Marcos Giménez de los Galanes, Alberto & García Portugués, Eduardo, 2022. "Data-driven stabilizations of goodness-of-fit tests," DES - Working Papers. Statistics and Econometrics. WS 35324, Universidad Carlos III de Madrid. Departamento de Estadística.
    10. Pham Ngoc, Thanh Mai, 2019. "Adaptive optimal kernel density estimation for directional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 248-267.
    11. Claudio Durastanti, 2016. "Quantitative central limit theorems for Mexican needlet coefficients on circular Poisson fields," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(4), pages 651-673, November.
    12. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    13. Marc Hallin & H Lui & Thomas Verdebout, 2022. "Nonparametric Measure-transportation-based Methods for Directional Data," Working Papers ECARES 2022-18, ULB -- Universite Libre de Bruxelles.

    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. Pham Ngoc, Thanh Mai, 2019. "Adaptive optimal kernel density estimation for directional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 248-267.
    2. Aboubacar Amiri & Baba Thiam & Thomas Verdebout, 2017. "On the Estimation of the Density of a Directional Data Stream," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 249-267, March.
    3. Barbeito, Inés & Cao, Ricardo, 2016. "Smoothed stationary bootstrap bandwidth selection for density estimation with dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 130-147.
    4. Paula Saavedra-Nieves & Rosa M. Crujeiras, 2022. "Nonparametric estimation of directional highest density regions," 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. 16(3), pages 761-796, September.
    5. Kim, Yoon Tae & Park, Hyun Suk, 2013. "Geometric structures arising from kernel density estimation on Riemannian manifolds," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 112-126.
    6. Jan Beran & Britta Steffens & Sucharita Ghosh, 2022. "On nonparametric regression for bivariate circular long-memory time series," Statistical Papers, Springer, vol. 63(1), pages 29-52, February.
    7. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    8. Heiler, Siegfried & Feng, Yuanhua, 1995. "A simple root n bandwidth selector for nonparametric regression," Discussion Papers, Series II 286, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    9. Graciela Boente & Daniela Rodriguez & Wenceslao González Manteiga, 2014. "Goodness-of-fit Test for Directional Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 259-275, March.
    10. J. M. Vilar & R. Cao & M. C. Ausin & C. Gonzalez-Fragueiro, 2009. "Nonparametric analysis of aggregate loss models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(2), pages 149-166.
    11. Bedouhene Kahina & Zougab Nabil, 2020. "A Bayesian procedure for bandwidth selection in circular kernel density estimation," Monte Carlo Methods and Applications, De Gruyter, vol. 26(1), pages 69-82, March.
    12. Charles C. Taylor & Kanti V. Mardia & Marco Di Marzio & Agnese Panzera, 2012. "Validating protein structure using kernel density estimates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2379-2388, July.
    13. Maria Jácome & Ricardo Cao, 2008. "Asymptotic-based bandwidth selection for the presmoothed density estimator with censored data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(6), pages 483-506.
    14. Klemelä, Jussi, 2000. "Estimation of Densities and Derivatives of Densities with Directional Data," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 18-40, April.
    15. Heiler, Siegfried & Feng, Yuanhua, 1997. "A bootstrap bandwidth selector for local polynomial fitting," Discussion Papers, Series II 344, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    16. Hall, Peter & Yatchew, Adonis, 2010. "Nonparametric least squares estimation in derivative families," Journal of Econometrics, Elsevier, vol. 157(2), pages 362-374, August.
    17. Isabel Fuentes-Santos & Wenceslao González-Manteiga & Jorge Mateu, 2016. "Consistent Smooth Bootstrap Kernel Intensity Estimation for Inhomogeneous Spatial Poisson Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 416-435, June.
    18. Nils-Bastian Heidenreich & Anja Schindler & Stefan Sperlich, 2013. "Bandwidth selection for kernel density estimation: a review of fully automatic selectors," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 403-433, October.
    19. Bose, Arup & Dutta, Santanu, 2013. "Density estimation using bootstrap bandwidth selector," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 245-256.
    20. Mercedes Fernandez Sau & Daniela Rodriguez, 2018. "Minimum distance method for directional data and outlier detection," 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. 12(3), pages 587-603, September.

    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:jmvana:v:121:y:2013:i:c:p:152-175. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.