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PDF(673 KB)
PDF(673 KB)
带超级光滑噪声密度函数的小波自适应点态估计
Wavelet Adaptive Pointwise Density Estimations with Super-smooth Noises
利用小波方法在局部Hölder空间中研究一类反卷积密度函数的点态估计问题.首先，针对超级光滑噪声给出该模型任一估计器的点态风险下界；其次，构造有限求和小波估计器，并证明其在超级光滑噪声条件下达到了最优收敛阶，即该估计器在点态风险下的收敛速度与下界一致.最后，还讨论了这类小波估计器的强收敛性.值得指出的是上述估计都是自适应的.
This paper considers pointwise deconvolution estimation of density functions under the local Hölder condition by wavelet method. We firstly give a lower bound of any estimator with super-smooth noises. Then the practical linear wavelet estimator is constructed to obtain the optimal convergence rate, which means that the rate coincides with the lower bound. The strong convergence rate of the defined wavelet estimator is also provided. It should be pointed out that all above estimations are adaptive.
小波 / 点态密度估计 / 自适应 / 最优性 {{custom_keyword}} /
wavelets / pointwise density estimation / adaptivity / optimality {{custom_keyword}} /
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国家自然科学基金（11771030）；北京市自然科学基金（1172001）；北京市博士后工作经费（ZZ2019-77）；北京工业大学基础研究基金（006000546319511，006000546319528）
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