A Fourier Approach to Nonparametric Deconvolution of a Density Estimate
A Fourier Approach to Nonparametric Deconvolution of a Density Estimate
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密度估计非参数反卷积的傅里叶方法
DOI：
10.1111/j.2517-6161.1993.tb01920.x
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
P. Hall
中科院分区：
文献类型：
--
作者：
P. Diggle;P. Hall
我们考虑的问题，构建一个非参数估计的概率密度函数h从独立的随机样本的观察密度a和f，当a表示卷积的h和f。我们的方法基于截断傅里叶逆，其中截断点扮演平滑参数的角色。我们推导出估计的渐近均方误差，并利用这个公式提出了一个简单实用的方法来选择截断点的数据。引人注目的是，当平滑参数以这种方式选择时，在许多情况下，估计量的行为，一阶，就好像真实的f是已知的
We consider the problem of constructing a nonparametric estimate of a probability density function h from independent random samples of observations from densities a and f, when a represents the convolution of h and f. Our approach is based on truncated Fourier inversion, in which the truncation point plays the role of a smoothing parameter. We derive the asymptotic mean integrated squared error of the estimate and use this formula to suggest a simple practical method for choosing the truncation point from the data. Strikingly, when the smoothing parameter is chosen in this way then in many circumstances the estimator behaves, to first order, as though the true f were known