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Anisotropic functional deconvolution for the irregular design: A minimax study

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  • Rida Benhaddou

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.

Suggested Citation

  • Rida Benhaddou, 2022. "Anisotropic functional deconvolution for the irregular design: A minimax study," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(13), pages 4589-4601, June.
    • Handle: RePEc:taf:lstaxx:v:51:y:2022:i:13:p:4589-4601
    DOI: 10.1080/03610926.2020.1818783
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