WIAS Preprint No. 398, (1998)

Wavelet method and asymptotically minimax estimation of regression


Authors

  • Golubev, Georgii

2010 Mathematics Subject Classification

  • 62G05 62G20

Keywords

  • Minimax risk, entire analytic functions, wavelet method, hard thresholding

DOI

10.20347/WIAS.PREPRINT.398

Abstract

We attempt to recover a regression function from noisy data. It is assumed that the underlying function is a piecewise entire analytic function. Types and the number of singularities are assumed to be unknown. We show how to chose smoothing parameters and a wavelet basis to achieve the asymptotically minimax risk up to the constant.

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