Weighted halfspace depth
نویسندگان
چکیده
Generalised halfspace depth function is proposed. Basic properties of this depth function including the strong consistency are studied. We show, on several examples that our depth function may be considered to be more appropriate for nonsymetric distributions or for mixtures of distributions.
منابع مشابه
Weighted Data Depth and Its Properties
The paper deals with nonparametric methods for analysis of multivariate data. Generalization of the halfspace depth, so called weighted halfspace depth, is indroduced. We consider its properties with respect to the weight function in its definition. One particular property of our interest: points out of the support of probability measure should have depth equal to zero.
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A data depth is one of the most important concepts of nonparametric multivariate analysis. Several depth functions have been introduced since 1980. The halfspace depth is probably the most popular. This depth function has many desirable properties (they are stated in the general definition of statictical depth function). We show a way of generalization of the halfspace depth finding a broader c...
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Data depth functions are a generalization of one-dimensional order statistics and medians to real spaces of dimension greater than one; in particular, a data depth function quantifies the centrality of a point with respect to a data set or a probability distribution. One of the most commonly studied data depth functions is halfspace depth. It is of interest to computational geometers because it...
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ورودعنوان ژورنال:
- Kybernetika
دوره 46 شماره
صفحات -
تاریخ انتشار 2010