منابع مشابه
Generalization of Halfspace Depth
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...
متن کاملWeighted halfspace depth
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.
متن کاملError Probabilities for Halfspace Depth
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...
متن کاملHalfspace Depth and Regression Depth Characterize the empirical Distribution
For multivariate data, the halfspace depth function can be seen as a natural and affine equivariant generalization of the univariate empirical cdf. For any multivariate data set, we show that the resulting halfspace depth function completely determines the empirical distribution. We do this by actually reconstructing the data points from the depth contours. The data need not be in general posit...
متن کاملA Branch and Cut Algorithm for the Halfspace Depth Problem
In non-parametric statistics, no assumption is made about the probability distribution of the population, and the test statistics are usually based on the rank of the data. In multivariate data analysis, every data item consists of several elements (i.e. is an n-tuple). The concept of data depth in non-parametric multivariate statistics is the generalization of the univariate rank method. Given...
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ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 2001
ISSN: 0047-259X
DOI: 10.1006/jmva.2000.1929