Wavelets and Estimation of Discontinuous Functions

  • Authors:
  • L. L. Boiko

  • Affiliations:
  • Institute for Information Transmission Problems, RAS, Moscow

  • Venue:
  • Problems of Information Transmission
  • Year:
  • 2004

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Abstract

The paper considers the problem of estimating a signal with finitely many points of discontinuity from observations against white Gaussian noise. It is shown that, with an appropriate choice of a generator polynomial, an estimation method based on wavelets yields asymptotically minimax (up to a constant) estimates for functions sufficiently smooth outside the discontinuity points.