2018/11/22 by Rida Benhaddou, Qing Liu, Benhaddou, Rida +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #62G05 #62G08 #62G20 #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #Image and Signal Denoising Methods #Methodology (stat.ME) #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1811.10411
openalex publication_date 2018/11/22 · openalex created_date 2018/11/29 · openalex updated_date 2026/07/28
In the present paper, we consider the estimation of a periodic two-dimensional function f(⋅,⋅) based on observations from its noisy convolution, and convolution kernel g(⋅,⋅) unknown. We derive the minimax lower bounds for the mean squared error assuming that f belongs to certain Besov space and the kernel function g 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.