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Design optimal sampling plans for functional regression models

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  • Rha, Hyungmin
  • Kao, Ming-Hung
  • Pan, Rong

Abstract

Functional regression models are widely considered in practice. To make a precise statistical inference, a good sampling schedule for collecting informative functional data is needed. However, there has not been much research on the optimal sampling schedule design for functional regression model so far. To address this design issue, an efficient computational approach is proposed for generating the best sampling plan in the function-on-function linear regression setting. The obtained sampling plan allows a precise estimation of the predictor function and a precise prediction of the response function. The proposed approach can also be applied to identify the optimal sampling plan for the problem with scalar-on-function linear regression model. Through case studies, this approach is demonstrated to outperform the methods proposed in the previous studies.

Suggested Citation

  • Rha, Hyungmin & Kao, Ming-Hung & Pan, Rong, 2020. "Design optimal sampling plans for functional regression models," Computational Statistics & Data Analysis, Elsevier, vol. 146(C).
  • Handle: RePEc:eee:csdana:v:146:y:2020:i:c:s0167947320300165
    DOI: 10.1016/j.csda.2020.106925
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    References listed on IDEAS

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    1. Fang Yao & Hans-Georg Müller & Andrew J. Clifford & Steven R. Dueker & Jennifer Follett & Yumei Lin & Bruce A. Buchholz & John S. Vogel, 2003. "Shrinkage Estimation for Functional Principal Component Scores with Application to the Population Kinetics of Plasma Folate," Biometrics, The International Biometric Society, vol. 59(3), pages 676-685, September.
    2. 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.
    3. Hao Ji & Hans-Georg Müller, 2017. "Optimal designs for longitudinal and functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 859-876, June.
    4. Moein Saleh & Ming-Hung Kao & Rong Pan, 2017. "Design D-optimal event-related functional magnetic resonance imaging experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(1), pages 73-91, January.
    5. Ashish Sood & Gareth M. James & Gerard J. Tellis, 2009. "Functional Regression: A New Model for Predicting Market Penetration of New Products," Marketing Science, INFORMS, vol. 28(1), pages 36-51, 01-02.
    6. Park, So Young & Xiao, Luo & Willbur, Jayson D. & Staicu, Ana-Maria & Jumbe, N. L’ntshotsholé, 2018. "A joint design for functional data with application to scheduling ultrasound scans," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 101-114.
    7. Meihua Wu & Ana Diez†Roux & Trivellore E. Raghunathan & Brisa N. Sánchez, 2018. "FPCA†based method to select optimal sampling schedules that capture between†subject variability in longitudinal studies," Biometrics, The International Biometric Society, vol. 74(1), pages 229-238, March.
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    Cited by:

    1. Kao, Ming-Hung & Huang, Ping-Han, 2024. "Hybrid exact-approximate design approach for sparse functional data," Computational Statistics & Data Analysis, Elsevier, vol. 190(C).

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