Universal pointwise selection rule in multivariate function estimation

Research output: Contribution to journalArticlepeer-review


In this paper, we study the problem of pointwise estimation of a multivariate function. We develop a general pointwise estimation procedure that is based on selection of estimators from a large parameterized collection. An upper bound on the pointwise risk is established and it is shown that the proposed selection procedure specialized for different collections of estimators leads to minimax and adaptive minimax estimators in various settings.

Original languageEnglish
Pages (from-to)1150-1190
Number of pages41
Issue number4
StatePublished - Nov 2008


  • Adaptive estimation
  • Minimax risk
  • Optimal rates of convergence
  • Pointwise estimation

ASJC Scopus subject areas

  • Statistics and Probability


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