On the averaged stochastic approximation for linear regression

László Györfi, Harro Walk

Research output: Contribution to journalArticle

12 Citations (Scopus)


For a linear regression function the average of stochastic approximation with constant gain is considered. In case of ergodic observations almost sure convergence is proved, where the limit is biased with small bias for small gain. For independent and identically distributed observations and also under martingale and mixing assumptions, asymptotic normality with (n-1/2)-convergence order is obtained. In the martingale case the asymptotic covariance matrix is close to the optimum one if the gain is small.

Original languageEnglish
Pages (from-to)31-61
Number of pages31
JournalSIAM Journal on Control and Optimization
Issue number1
Publication statusPublished - Jan 1996


  • Adaptive filtering
  • Almost sure convergence
  • Asymptotic normality
  • Averaged stochastic approximation
  • Constant gains
  • Ergodicity
  • Linear regression
  • Martingales
  • Mixing

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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