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Optimal weighting schemes for longitudinal and functional data

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  • Zhang, Xiaoke
  • Wang, Jane-Ling

Abstract

We propose optimal weighting schemes for both mean and covariance estimations for functional data based on local linear smoothing such that the L2 rate of convergence is minimized. These schemes can self-adjust to the sampling plan and lead to practical improvements.

Suggested Citation

  • Zhang, Xiaoke & Wang, Jane-Ling, 2018. "Optimal weighting schemes for longitudinal and functional data," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 165-170.
    • Handle: RePEc:eee:stapro:v:138:y:2018:i:c:p:165-170
    DOI: 10.1016/j.spl.2018.03.007
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    References listed on IDEAS

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    1. Philip T. Reiss & Jeff Goldsmith & Han Lin Shang & R. Todd Ogden, 2017. "Methods for Scalar-on-Function Regression," International Statistical Review, International Statistical Institute, vol. 85(2), pages 228-249, August.
    2. Kokoszka, Piotr & Oja, Hanny & Park, Byeong & Sangalli, Laura, 2017. "Special issue on functional data analysis," Econometrics and Statistics, Elsevier, vol. 1(C), pages 99-100.
    3. Manteiga, Wenceslao Gonzalez & Vieu, Philippe, 2007. "Statistics for Functional Data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4788-4792, June.
    4. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    5. repec:wyi:journl:002174 is not listed on IDEAS
    6. Luo Xiao & Yingxing Li & David Ruppert, 2013. "Fast bivariate P-splines: the sandwich smoother," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 577-599, June.
    7. Jianhua Z. Huang, 2002. "Varying-coefficient models and basis function approximations for the analysis of repeated measurements," Biometrika, Biometrika Trust, vol. 89(1), pages 111-128, March.
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    Cited by:

    1. Hassan Sharghi Ghale-Joogh & S. Mohammad E. Hosseini-Nasab, 2021. "On mean derivative estimation of longitudinal and functional data: from sparse to dense," Statistical Papers, Springer, vol. 62(4), pages 2047-2066, August.
    2. Xiongtao Dai & Zhenhua Lin & Hans‐Georg Müller, 2021. "Modeling sparse longitudinal data on Riemannian manifolds," Biometrics, The International Biometric Society, vol. 77(4), pages 1328-1341, December.

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