This paper considers multivariate deconvolution density estimations under the local Hölder condition by wavelet methods. A pointwise lower bound of the deconvolution model is first investigated; then we provide a linear wavelet estimate to obtain the optimal convergence rate. The nonlinear wavelet estimator is introduced for adaptivity, which attains a nearly optimal rate (optimal up to a logarithmic factor). Because the nonlinear wavelet estimator depends on an upper bound of the smoothness index of unknown functions, we finally discuss a data-driven version without any assumption on the estimated functions.

中文翻译：

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小波自适应和最佳逐点解卷积密度估计

本文考虑了在局部Hölder条件下通过小波方法进行的多变量反卷积密度估计。首先研究反卷积模型的逐点下界。然后提供线性小波估计以获得最佳收敛速度。为适应性引入了非线性小波估计器，该方法获得了近乎最佳的速率（最高达对数因子）。由于非线性小波估计器取决于未知函数的平滑度指数的上限，因此我们最终讨论了一种数据驱动版本，而无需对估计函数进行任何假设。