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Optimal prediction for linear regression with infinitely many parameters

Author

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  • Goldenshluger, Alexander
  • Tsybakov, Alexandre

Abstract

The problem of optimal prediction in the stochastic linear regression model with infinitely many parameters is considered. We suggest a prediction method that outperforms asymptotically the ordinary least squares predictor. Moreover, if the random errors are Gaussian, the method is asymptotically minimax over ellipsoids in l2. The method is based on a regularized least squares estimator with weights of the Pinsker filter. We also consider the case of dynamic linear regression, which is important in the context of transfer function modeling.

Suggested Citation

  • Goldenshluger, Alexander & Tsybakov, Alexandre, 2003. "Optimal prediction for linear regression with infinitely many parameters," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 40-60, January.
    • Handle: RePEc:eee:jmvana:v:84:y:2003:i:1:p:40-60
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    Cited by:

    1. Comte , Fabienne & Johannes, Jan, 2011. "Adaptive functional linear regression," LIDAM Discussion Papers ISBA 2011038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. T. Tony Cai & Mark Low & Linda Zhao, 2009. "Sharp adaptive estimation by a blockwise method," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(7), pages 839-850.

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