Estimation of Support of a Density

  • A. P. Korostelev
  • A. B. Tsybakov
Part of the Lecture Notes in Statistics book series (LNS, volume 82)

Abstract

Let X1,…,Xn be i.i.d. random variables uniformly distributed in a closed set G ⊂ K=[0/1]N , mes G ≠ 0. In this chapter we study the problem of estimation of G, given the observations X1,…,Xn . This problem is closely related to edge estimation, and, as we show later, it can be solved by similar means. The minimax convergence rates for estimators of supports with smooth boundaries turn out to be the same as those for edge estimators (cf. Chapters 4, 5).

Keywords

Hull 

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Copyright information

© Springer-Verlag New York, Inc. 1993

Authors and Affiliations

  • A. P. Korostelev
    • 1
  • A. B. Tsybakov
    • 2
  1. 1.Institute for Systems StudiesMoscowRussia
  2. 2.Institute for Problems of Information TransmissionMoscow GSP-4Russia

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