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Functional linear model

Author

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  • Cardot, Hervé
  • Ferraty, Frédéric
  • Sarda, Pascal

Abstract

In this paper, we study a regression model in which explanatory variables are sampling points of a continuous-time process. We propose an estimator of regression by means of a Functional Principal Component Analysis analogous to the one introduced by Bosq [(1991) NATO, ASI Series, pp. 509-529] in the case of Hilbertian AR processes. Both convergence in probability and almost sure convergence of this estimator are stated.

Suggested Citation

  • Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    • Handle: RePEc:eee:stapro:v:45:y:1999:i:1:p:11-22
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    References listed on IDEAS

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    1. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
    2. Yurinskii, V. V., 1976. "Exponential inequalities for sums of random vectors," Journal of Multivariate Analysis, Elsevier, vol. 6(4), pages 473-499, December.
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