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On mean derivative estimation of longitudinal and functional data: from sparse to dense

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  • Hassan Sharghi Ghale-Joogh

    (Shahid Beheshti University)

  • S. Mohammad E. Hosseini-Nasab

    (Shahid Beheshti University)

Abstract

Derivative estimation of the mean of longitudinal and functional data is useful, because it provides a quantitative measure of changes in the mean function that can be used for modeling of the data. We propose a general method for estimation of the derivative of the mean function that allows us to make inference about both longitudinal and functional data regardless of the sparsity of data. The $$L^2$$ L 2 and uniform convergence rates of the local linear estimator for the true derivative of the mean function are derived. Then the optimal weighting scheme under the $$L^2$$ L 2 rate of convergence is obtained. The performance of the proposed method is evaluated by a simulation study, and additionally compared with another existing method. The method is used to analyse a real data set involving children weight growth failure.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:4:d:10.1007_s00362-020-01173-5
    DOI: 10.1007/s00362-020-01173-5
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    References listed on IDEAS

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