Abstract
In the convolution model Z i = X i + ε i , we give a model selection procedure to estimate the density of the unobserved variables (X i )1≤i≤n , when the sequence (X i ) i≥1 is strictly stationary but not necessarily independent. This procedure depends on whether the density of the ɛ i is supersmooth or ordinary smooth. The rates of convergence of the penalized contrast estimators are the same as in the independent framework, and are minimax over most regularity classes on ℝ. Our results apply to mixing sequences, but also to many other dependent sequences. When the errors are supersmooth, the condition on the dependence coefficients is the minimal condition of that type ensuring that the sequence (X i ) i≥1 is not a long-memory process.
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Comte, F., Dedecker, J. & Taupin, M.L. Adaptive density deconvolution with dependent inputs. Math. Meth. Stat. 17, 87–112 (2008). https://doi.org/10.3103/S1066530708020014
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DOI: https://doi.org/10.3103/S1066530708020014