ResearchTrend.AI
  • Papers
  • Communities
  • Events
  • Blog
  • Pricing
Papers
Communities
Social Events
Terms and Conditions
Pricing
Parameter LabParameter LabTwitterGitHubLinkedInBlueskyYoutube

© 2025 ResearchTrend.AI, All rights reserved.

  1. Home
  2. Papers
  3. 1811.10411
36
1
v1v2 (latest)

Minimax adaptive wavelet estimator for the anisotropic functional deconvolution model with unknown kernel

22 November 2018
Rida Benhaddou
Qing Liu
ArXiv (abs)PDFHTML
Abstract

In the present paper, we consider the estimation of a periodic two-dimensional function f(⋅,⋅)f(\cdot,\cdot)f(⋅,⋅) based on observations from its noisy convolution, and convolution kernel g(⋅,⋅)g(\cdot,\cdot)g(⋅,⋅) unknown. We derive the minimax lower bounds for the mean squared error assuming that fff belongs to certain Besov space and the kernel function ggg satisfies some smoothness properties. We construct an adaptive hard-thresholding wavelet estimator that is asymptotically near-optimal within a logarithmic factor in a wide range of Besov balls. The proposed estimation algorithm implements a truncation to estimate the wavelet coefficients, in addition to the conventional hard-thresholds. A limited simulations study confirms theoretical claims of the paper.

View on arXiv
Comments on this paper