## Abstract

Fix m, n ≥ 1. Given an N-point set E ⊂ R{double-struck}^{n}, we exhibit a list of O (N) subsets S_{1}, S_{2},..., S_{L} ⊂ 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_{ℓ} ∈ C^{m} (R{double-struck}^{n}) with norm ≤ 1, agreeing with f on S_{ℓ} Then there exists F ∈ C^{m} (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 language | English (US) |
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Pages (from-to) | 427-441 |

Number of pages | 15 |

Journal | Annals of Mathematics |

Volume | 170 |

Issue number | 1 |

DOIs | |

State | Published - 2009 |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

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