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Joint estimation of monotone curves via functional principal component analysis

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  • Shin, Yei Eun
  • Zhou, Lan
  • Ding, Yu

Abstract

A functional data approach is developed to jointly estimate a collection of monotone curves that are irregularly and possibly sparsely observed with noise. In this approach, the unconstrained relative curvature curves instead of the monotone-constrained functions are directly modeled. Functional principal components are used to describe the major modes of variations of curves and allow borrowing strength across curves for improved estimation. A two-step approach and an integrated approach are considered for model fitting. The simulation study shows that the integrated approach is more efficient than separate curve estimation and the two-step approach. The integrated approach also provides more interpretable principle component functions in an application of estimating weekly wind power curves of a wind turbine.

Suggested Citation

  • Shin, Yei Eun & Zhou, Lan & Ding, Yu, 2022. "Joint estimation of monotone curves via functional principal component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:csdana:v:166:y:2022:i:c:s0167947321001778
    DOI: 10.1016/j.csda.2021.107343
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    References listed on IDEAS

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    1. J. O. Ramsay, 1998. "Estimating smooth monotone functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 365-375.
    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. Hall, Peter & Muller, Hans-Georg, 2003. "Order-Preserving Nonparametric Regression, With Applications to Conditional Distribution and Quantile Function Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 598-608, January.
    4. John A. Rice & Colin O. Wu, 2001. "Nonparametric Mixed Effects Models for Unequally Sampled Noisy Curves," Biometrics, The International Biometric Society, vol. 57(1), pages 253-259, March.
    5. Philippe Besse & J. Ramsay, 1986. "Principal components analysis of sampled functions," Psychometrika, Springer;The Psychometric Society, vol. 51(2), pages 285-311, June.
    6. Lan Zhou & Jianhua Z. Huang & Raymond J. Carroll, 2008. "Joint modelling of paired sparse functional data using principal components," Biometrika, Biometrika Trust, vol. 95(3), pages 601-619.
    7. Besse, Philippe C. & Cardot, Herve & Ferraty, Frederic, 1997. "Simultaneous non-parametric regressions of unbalanced longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 24(3), pages 255-270, May.
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