Wavelet Estimation of Function Derivatives from a Multichannel Deconvolution Model. (31st December 2022)

• Record Type: Journal Article
• Authors: Guo, Huijun; Li, Shuzi
• Other Names: Nicolay Samuel Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-12-31
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/2075229
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : This paper considers a multichannel deconvolution model with Gaussian white noises. The goal is to estimate the d -th derivatives of an unknown function in the model. For super-smooth case, we construct an adaptive linear wavelet estimator by wavelet projection method. For regular-smooth case, we provide an adaptive nonlinear wavelet estimator by hard-thresholded method. In order to measure the global performances of our estimators, we show upper bounds on convergence rates using the L p -risk (1 ≤ p < ∞ ).