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This note considers an n-letter alphabet in which the ith letter is accessed with probability p_i. The problem is to design efficient algorithm for constructing near-optimal, depth-constrained Huffman...
We enlarge the available number of functional depths by defining two new depth measures for curves. Both depths are based on a spatial approach: the functional spatial depth (FSD), that shows an inter...
We generalize recent theoretical work on the minimal number of layers of narrow deep belief networks that can approximate any probability distribution on the states of their visible units arbitrarily ...
Depth statistics     Depth statistics       2012/9/19
In 1975 John Tukey proposed a multivariate median which is the ‘deepest’ point in a given data cloud in Rd(Tukey, 1975). In measuring the depth of an arbitrary pointzwith respect to the data, he consi...
A new procedure, calledDDα-procedure, is developed to solve the problem of classifyingd-dimensional objects into q≥2 classes. The pro-cedure is completely nonparametric; it usesq-dimensional depth plo...
A data depth measures the centrality of a point with respect to an empirical distribution. Postulates are formulated, which a depth for functional data should satisfy, and a general approach is propos...
A new multivariate concept of quantile, based on a directional version of Koenker and Bassett’s traditional regression quantiles, is introduced for multivariate location and multiple-output regressi...
First I would like to congratulate the authors for developing a new concept of directional quantile contours. The work will contribute well to the pursuit of multivariate quantiles. The multiple out...
In interviewing in the hiring of personnel has recently been reassessed. Formerly, interview techniques were criticised as being unreliable and invalid. Now, meta analysis indicates that a structured ...
The computation of the Tukey depth, also called halfspace depth, is very demanding, even in low dimensional spaces, because it requires the consideration of all possible one-dimensional projections.I...
As estimators of location parameters, univariate trimmed means are well known for their robustness and efficiency. They can serve as robust alternatives to the sample mean while possessing high effi...

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