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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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    1. Liu, Bitao & Müller, Hans-Georg, 2009. "Estimating Derivatives for Samples of Sparsely Observed Functions, With Application to Online Auction Dynamics," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 704-717.
    2. Ling Zhou & Huazhen Lin & Hua Liang, 2018. "Efficient Estimation of the Nonparametric Mean and Covariance Functions for Longitudinal and Sparse Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1550-1564, October.
    3. Jianqing Fan & Wenyang Zhang, 2000. "Simultaneous Confidence Bands and Hypothesis Testing in Varying‐coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 715-731, December.
    4. Kara, Lydia-Zaitri & Laksaci, Ali & Rachdi, Mustapha & Vieu, Philippe, 2017. "Data-driven kNN estimation in nonparametric functional data analysis," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 176-188.
    5. Honglang Wang & Ping‐Shou Zhong & Yuehua Cui & Yehua Li, 2018. "Unified empirical likelihood ratio tests for functional concurrent linear models and the phase transition from sparse to dense functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(2), pages 343-364, March.
    6. Shuzhuan Zheng & Lijian Yang & Wolfgang K. Härdle, 2014. "A Smooth Simultaneous Confidence Corridor for the Mean of Sparse Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 661-673, June.
    7. Yixin Chen & Weixin Yao, 2017. "Unified Inference for Sparse and Dense Longitudinal Data in Time-varying Coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 268-284, March.
    8. Zhang, Xiaoke & Wang, Jane-Ling, 2018. "Optimal weighting schemes for longitudinal and functional data," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 165-170.
    9. Pini, Alessia & Spreafico, Lorenzo & Vantini, Simone & Vietti, Alessandro, 2019. "Multi-aspect local inference for functional data: Analysis of ultrasound tongue profiles," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 162-185.
    10. Juxia Xiao & Xu Li & Jianhong Shi, 2019. "Local linear smoothers using inverse Gaussian regression," Statistical Papers, Springer, vol. 60(4), pages 1225-1253, August.
    11. N. Hosseinioun & H. Doosti & H. Nirumand, 2012. "Nonparametric estimation of the derivatives of a density by the method of wavelet for mixing sequences," Statistical Papers, Springer, vol. 53(1), pages 195-203, February.
    12. Wanrong Liu & Xuewen Lu, 2011. "Empirical likelihood for density-weighted average derivatives," Statistical Papers, Springer, vol. 52(2), pages 391-412, May.
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