Wavelet method and asymptotically minimax estimation of regression
- Golubev, Georgii
2010 Mathematics Subject Classification
- 62G05 62G20
- Minimax risk, entire analytic functions, wavelet method, hard thresholding
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.