|Title||Asymptotic estimate of depth-based classifiers within the location shift model|
|Publication Type||Journal Article|
|Year of Publication||2015|
|Abbreviated Key Title||Dopov. Nac. akad. nauk Ukr.|
|Section||Information Science and Cybernetics|
The asymptotic behavior of non-parametric simplicial depth, half-space depth, and spatial depth classifiers is studied under appropriate regularity conditions. The research is carried out for the construction of a maximum depth classifier, when all a priori probabilities of all the competing classes are equal, and the location shift model holds. The constructed maximum depth classifier does not depend on the special parametric form of the dividing surface and classifies the data item to a class, with respect to which the element has a maximum depth of location. The case of unequal a priori probabilities is studied, when different data sets may not belong to the common family of elliptical distributions.
|Keywords||Bayesian classifier, depth function, Mahalanobis distance|
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