An Iterative Method for Estimating a Multivariate Mode and Isopleth
An Iterative Method for Estimating a Multivariate Mode and Isopleth
复制标题
估计多元模态和等值线的迭代方法
DOI：
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发表时间：
1979
期刊：
影响因子：
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通讯作者：
T. Sager
中科院分区：
文献类型：
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作者：
T. Sager
摘要提出了一种估计多元分布的众数和等值线的迭代方法。该模式是通过选择一个点，从最后一组嵌套递减序列的凸集，其中每一个迭代的最小封闭，凸子集包含一定比例的其前任的数据点。等值线由对应于固定迭代次数（与n无关）的凸子集的边界估计。该方法产生一个自然的密度估计。估计几乎肯定收敛，并给出了一元等值线估计的收敛速度。注意到在空气污染和健康科学方面的应用。
Abstract An iterative procedure for estimating the mode and isopleths of a multivariate distribution is presented. The mode is estimated by selecting a point from the final set in a nested decreasing sequence of convex sets, each one of which is iteratively the smallest closed, convex subset containing a certain proportion of its predecessor's data points. An isopleth is estimated by the boundary of the convex subset corresponding to a fixed number of iterations (independent of n). The method gives rise to a natural density estimator. The estimators are shown to converge almost surely, and convergence rates for the univariate isopleth estimator are presented. Applications to air pollution and health sciences are noted.