IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v99y2015icp156-166.html
   My bibliography  Save this article

Estimating with kernel smoothers the mean of functional data in a finite population setting. A note on variance estimation in presence of partially observed trajectories

Author

Listed:
  • Cardot, Hervé
  • De Moliner, Anne
  • Goga, Camelia

Abstract

This paper studies, in a survey sampling framework with unequal probability sampling designs, three nonparametric kernel estimators for the mean curve in presence of discretized trajectories with missing values. Their pointwise variances are approximated thanks to linearization techniques.

Suggested Citation

  • Cardot, Hervé & De Moliner, Anne & Goga, Camelia, 2015. "Estimating with kernel smoothers the mean of functional data in a finite population setting. A note on variance estimation in presence of partially observed trajectories," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 156-166.
    • Handle: RePEc:eee:stapro:v:99:y:2015:i:c:p:156-166
    DOI: 10.1016/j.spl.2015.01.025
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715215000310
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2015.01.025?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. Hervé Cardot & Etienne Josserand, 2011. "Horvitz--Thompson estimators for functional data: asymptotic confidence bands and optimal allocation for stratified sampling," Biometrika, Biometrika Trust, vol. 98(1), pages 107-118.
    2. Hart, Jeffrey D. & Wehrly, Thomas E., 1993. "Consistency of cross-validation when the data are curves," Stochastic Processes and their Applications, Elsevier, vol. 45(2), pages 351-361, April.
    3. K. Vind, 1971. "Comment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(1), pages 115-115.
    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. Ferreira, Eva & Núñez-Antón, Vicente & Rodríguez-Póo, Juan, 1997. "Kernel regression estimates of growth curves using nonstationary correlated errors," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 413-423, June.
    2. Gattone, Stefano Antonio & Fortuna, Francesca & Evangelista, Adelia & Di Battista, Tonio, 2022. "Simultaneous confidence bands for the functional mean of convex curves," Econometrics and Statistics, Elsevier, vol. 24(C), pages 183-193.
    3. Wang, Jianqiang C., 2012. "Sample distribution function based goodness-of-fit test for complex surveys," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 664-679.
    4. Serfling, Robert & Wijesuriya, Uditha, 2017. "Depth-based nonparametric description of functional data, with emphasis on use of spatial depth," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 24-45.
    5. Devine, James G., 2011. "The great moderation and "falling off a cliff": Neo-Kaldorian dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 366-373, May.
    6. Li, Hongbin & Zhang, Jie & Zhang, Junsen, 2007. "Effects of longevity and dependency rates on saving and growth: Evidence from a panel of cross countries," Journal of Development Economics, Elsevier, vol. 84(1), pages 138-154, September.
    7. Vicente Núñez-Antón & Juan Rodríguez-Póo & Philippe Vieu, 1999. "Longitudinal data with nonstationary errors: a nonparametric three-stage approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 201-231, June.
    8. repec:ags:nbaesp:140460 is not listed on IDEAS
    9. Hervé Cardot & Camelia Goga & Pauline Lardin, 2014. "Variance Estimation and Asymptotic Confidence Bands for the Mean Estimator of Sampled Functional Data with High Entropy Unequal Probability Sampling Designs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 516-534, June.
    10. Maria del Mar Rueda, 2019. "Comments on: Deville and Särndal’s calibration: revisiting a 25 years old successful optimization problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1077-1081, December.
    11. Kivilcim Metin Ozcan & Asli Gunay & Seda Ertac, 2003. "Determinants of private savings behaviour in Turkey," Applied Economics, Taylor & Francis Journals, vol. 35(12), pages 1405-1416.
    12. Colin Wu & Xin Tian & Jarvis Yu, 2010. "Nonparametric estimation for time-varying transformation models with longitudinal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 133-147.
    13. Chateau, Jean-Pierre D., 1977. "Une analyse économétrique du comportement d’intermédiation financière des sociétés de crédit populaire : le cas des caisses populaires," L'Actualité Economique, Société Canadienne de Science Economique, vol. 53(3), pages 415-447, juillet.
    14. Diane Macunovich, 1999. "The Baby Boom As It Ages: How Has It Affected Patterns of Consumptions and Savings in the United States?," Center for Policy Research Working Papers 7, Center for Policy Research, Maxwell School, Syracuse University.
    15. Colin O. Wu & Kai F. Yu, 2002. "Nonparametric Varying-Coefficient Models for the Analysis of Longitudinal Data," International Statistical Review, International Statistical Institute, vol. 70(3), pages 373-393, December.
    16. Ahmed, M.S. & Attouch, M.K. & Dabo-Niang, S., 2018. "Binary functional linear models under choice-based sampling," Econometrics and Statistics, Elsevier, vol. 7(C), pages 134-152.
    17. Wang, Jiangyan & Gu, Lijie & Yang, Lijian, 2022. "Oracle-efficient estimation for functional data error distribution with simultaneous confidence band," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    18. Gerard, Patrick D. & Schucany, William R., 1996. "On combining independent nonparametric regression estimators," Statistics & Probability Letters, Elsevier, vol. 26(1), pages 25-34, January.
    19. Aylit T. Romm & Martha Wolny, 2012. "The Impact of Later Retirement Ages on Aggregate Household Savings and Saving Rates: An Analysis of OECD Countries," Working Papers 269, Economic Research Southern Africa.
    20. Johan Fourie, 2012. "The wealth of the Cape Colony: Measurements from probate inventories," Working Papers 268, Economic Research Southern Africa.

    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:stapro:v:99:y:2015:i:c:p:156-166. 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.