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Linear prediction in functional data analysis

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  • Shin, Hyejin
  • Hsing, Tailen

Abstract

In this paper we introduce a new perspective of linear prediction in the functional data context that predicts a scalar response by observing a functional predictor. This perspective broadens the scope of functional linear prediction currently in the literature, which is exclusively focused on the functional linear regression model. It also provides a natural link to the classical linear prediction theory. Based on this formulation, we derive the convergence rate of the optimal mean squared predictor.

Suggested Citation

  • Shin, Hyejin & Hsing, Tailen, 2012. "Linear prediction in functional data analysis," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3680-3700.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:11:p:3680-3700
    DOI: 10.1016/j.spa.2012.06.014
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    References listed on IDEAS

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    1. Cardot, Hervé & Johannes, Jan, 2010. "Thresholding projection estimators in functional linear models," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 395-408, February.
    2. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    3. Cardot, Herve & Johannes, Jan, 2010. "Thresholding projection estimators in functional linear models," LIDAM Reprints ISBA 2010034, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    Citations

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    Cited by:

    1. Kraus, David & Stefanucci, Marco, 2020. "Ridge reconstruction of partially observed functional data is asymptotically optimal," Statistics & Probability Letters, Elsevier, vol. 165(C).
    2. Wang, Jiangyan & Gu, Lijie & Yang, Lijian, 2022. "Oracle-efficient estimation for functional data error distribution with simultaneous confidence band," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    3. José R. Berrendero & Beatriz Bueno-Larraz & Antonio Cuevas, 2023. "On functional logistic regression: some conceptual issues," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 321-349, March.
    4. Sylvain Robbiano & Matthieu Saumard & Michel Curé, 2016. "Improving prediction performance of stellar parameters using functional models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(8), pages 1465-1476, June.
    5. José R. Berrendero & Alejandro Cholaquidis & Antonio Cuevas, 2024. "On the functional regression model and its finite-dimensional approximations," Statistical Papers, Springer, vol. 65(8), pages 5167-5201, October.
    6. Asma Ben Saber & Abderrazek Karoui, 2024. "On some stable linear functional regression estimators based on random projections," Statistical Papers, Springer, vol. 65(7), pages 4147-4178, September.

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