Asymptotic behavior of the grenander estimator at density flat regions
Asymptotic behavior of the grenander estimator at density flat regions
复制标题
密度平坦区域的 grenander 估计器的渐近行为
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
R. Dykstra
中科院分区：
文献类型：
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作者：
C. Carolan;R. Dykstra
四十多年前，Grenander通过已知模式衍生了单调的MLE，Prakasa Rao在固定点X上获得了该估计值的渐近分布，其中F'（x）<0。当f恒定时，固定点x的估计器在x的某些开放型邻域中是封闭式密度的卷积和降低的标准正常状态时表达的。密度。Groeneboom（1983）得出了近似闭合形式的密度，我们提供了一种更直接的推导。
Over forty years ago, Grenander derived the MLE of a monotone decreasing density f with known mode. Prakasa Rao obtained the asymptotic distribution of this estimator at a fixed point x where f' (x) < 0. Here, we obtain the asymptotic distribution of this estimator at a fixed point x when f is constant and nonzero in some open neighborhood of x. This limiting distribution is expressible as the convolution of a closed‐form density and a rescaled standard normal density. Groeneboom (1983) derived the aforementioned closed‐form density and we provide an alternative, more direct derivation.