Optimal prediction for linear regression with infinitely many parameters |
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Authors: | Alexander Goldenshluger |
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Institution: | a Department of Statistics, University of Haifa, Haifa 31905, Israel b Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI, BP 188, 4 place Jussieu, Paris 75252, Cedex 05, France |
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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 ?2. 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. |
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Keywords: | 62G05 62G20 |
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