NONPARAMETRIC DENSITY-ESTIMATION WITH A PARAMETRIC START
NONPARAMETRIC DENSITY-ESTIMATION WITH A PARAMETRIC START
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DOI：
10.1214/aos/1176324627
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发表时间：
1995-06-01
影响因子：
4.5
通讯作者：
GLAD, IK
中科院分区：
文献类型：
--
作者：
HJORT, NL;GLAD, IK
传统的核密度估计的一个未知的密度是通过建设完全非参数的意义上说，它没有偏好，并将合理地为所有形状。本论文开发了一类半参数方法，其设计比核估计更好地工作在一个广泛的非参数邻域的一个给定的参数类的密度，例如，正常的，而不会失去太多的精度时，真密度是远离参数类。其思想是将初始参数密度估计与必要的校正因子的核类型估计相乘。这在校正因子函数比原始密度本身不那么粗糙的情况下工作得很好。与核估计进行了广泛的比较，包括所有正常的混合物类的精确分析。新的方法，在一个正常的开始，赢得了相当频繁，即使在许多情况下，真正的密度是远离正常。本文还讨论了估计量中平滑参数的选取方法。新的估计应该是特别有用的，在高维，通常的非参数方法有问题。这个想法也被阐述为非参数回归。
The traditional kernel density estimator of an unknown density is by construction completely nonparametric in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of semiparametric methods that are designed to work better than the kernel estimator in a broad nonparametric neighbourhood of a given parametric class of densities, for example, the normal, while not losing much in precision when the true density is far from the parametric class. The idea is to multiply an initial parametric density estimate with a kernel-type estimate of the necessary correction factor. This works well in cases where the correction factor function is less rough than the original density itself. Extensive comparisons with the kernel estimator are carried out; including exact analysis for the class of all normal mixtures. The new method, with a normal start, wins quite often, even in many cases where the true density is far from normal. Procedures for choosing the smoothing parameter of the estimator are also discussed. The new estimator should be particularly useful in higher dimensions, where the usual nonparametric methods have problems. The idea is also spelled out for nonparametric regression.