Fitting a Cm-smooth function to data, III

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Fix m, n ≥ 1. Given an N-point set E ⊂ R{double-struck}n, we exhibit a list of O (N) subsets S1, S2,..., SL ⊂ E, each containing O (1) points, such that the following holds: Let f: E → R{double-struck}n. Suppose that, for each ℓ = 1,..., L, there exists F ∈ Cm (R{double-struck}n) with norm ≤ 1, agreeing with f on S Then there exists F ∈ Cm (R{double-struck}n) with norm O (1), agreeing with f on E. We give an application to the problem of discarding outliers from the set E.

Original languageEnglish (US)
Pages (from-to)427-441
Number of pages15
JournalAnnals of Mathematics
Issue number1
StatePublished - 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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