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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

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  • 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
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    References listed on IDEAS

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    1. K. Vind, 1971. "Comment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(1), pages 115-115.
    2. 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.
    3. 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.
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