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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.
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