Continuity of Halfspace Depth Contours and Maximum Depth Estimators: Diagnostics of Depth-Related Methods
نویسندگان
چکیده
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 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 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 کاملProximity graph depth, depth contours, and a new multimodal median
We propose proximity graph depth as a class of depth functions, based on the minimum path length along proximity graph edges to the convex hull of a point set. We analyze the characteristics of several proximity graph depth functions both theoretically and experimentally, define depth contours enclosing regions of increasing depth, and present algorithms for calculating depth values in a point ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 2002
ISSN: 0047-259X
DOI: 10.1006/jmva.2001.2053