Anisotropic functional deconvolution for the irregular design: A minimax study

Rida Benhaddou

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 13, 4589-4601

Abstract: Anisotropic functional deconvolution model is investigated in the bivariate case when the design points ti, i=1,2,⋯,N, and xl, l=1,2,⋯,M, are irregular and follow known densities h1, h2, respectively. In particular, we focus on the case when the densities h1 and h2 have singularities, but 1/h1 and 1/h2 are still integrable on [0, 1]. We construct an adaptive wavelet estimator that attains asymptotically near-optimal convergence rates in a wide range of Besov balls. The convergence rates are completely new and depend on a balance between the smoothness and the spatial homogeneity of the unknown function f, the degree of ill-posed-ness of the convolution operator and the degrees of spatial irregularity associated with h1 and h2. Nevertheless, the spatial irregularity affects convergence rates only when f is spatially inhomogeneous in either direction.

Date: 2022
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DOI: 10.1080/03610926.2020.1818783

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