Optimal prediction for linear regression with infinitely many parameters

Alexander Goldenshluger, Alexandre Tsybakov

Research output: Contribution to journalReview articlepeer-review


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.

Original languageEnglish
Pages (from-to)40-60
Number of pages21
JournalJournal of Multivariate Analysis
Issue number1
StatePublished - Jan 2003

Bibliographical note

Funding Information:
The research was supported in part by a Grant of the ESF programme on “Highly Structured Stochastic Systems (HSSS)” and by a Grant of the Arc-en-ciel/Keshet program.


  • Exact asymptotics of minimax risk
  • Linear regression with infinitely many parameters
  • Optimal prediction
  • Pinsker filter

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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