AN ALTERNATIVE UNIMODAL DENSITY ESTIMATOR WITH A CONSISTENT ESTIMATE OF THE MODE
AN ALTERNATIVE UNIMODAL DENSITY ESTIMATOR WITH A CONSISTENT ESTIMATE OF THE MODE
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发表时间：
1999
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通讯作者：
Mary C. Meyer
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作者：
Mary C. Meyer
传统的最大似然单峰密度估计（Grenander（1956））在一个已知的模式下将两个保序密度估计拼凑在一起。它在模态处是不连续的，不能直接适应未知模态的情况。本文提出了一种可供选择的单峰密度估计的形式广义保序回归偏序是连续的模式，并很容易移动到未知模式的情况下。引入了一种惩罚形式来控制该模式下的尖峰，并证明了该惩罚形式在任何地方都是一致的。结果表明，惩罚估计也提供了一个一致的估计模式。仿真结果比较惩罚估计到其他非参数估计在文献中的Hellinger距离，平方误差损失的估计模式，和高度的模式。新估计器的两个重要优点是，它同时提供密度估计和模式估计，并且它是“全自动的”，即，没有预先分组或密度高度的界限是必要的，以防止尖峰。
The traditional maximum likelihood unimodal density estimator (Grenander (1956)) pieces together two isotonic density estimators at a known mode. It is discontinuous at the mode, and does not directly adapt to the case of unknown mode. This paper presents an alternative unimodal density estimator in the form of a generalized isotonic regression on a partial order which is continuous at the mode, and moves easily to the case of unknown mode. A penalized version is introduced to control the spiking at the mode, and is proved to be consistent everywhere. It is shown that the penalized estimator also provides a consistent estimate of the mode. Simulation results compare the penalized estimator to other nonparametric estimators in the literature in terms of Hellinger distance, the squared error loss of the estimate of the mode, and the height at the mode. Two important advantages of the new estimator are that it provides the density estimate and the mode estimate simultaneously, and that it is “fully automatic,” that is, no pre-grouping or bounds on density height are necessary to prevent spiking.