On Maximum Depth and Related Classifiers

Authors: GHOSH, ANIL K.¹; CHAUDHURI, PROBAL²

Source: Scandinavian Journal of Statistics, Volume 32, Number 2, June 2005 , pp. 327-350(24)

Buy & download fulltext article:

Price: $48.00 plus tax (Refund Policy)

Abstract:

Over the last couple of decades, data depth has emerged as a powerful exploratory and inferential tool for multivariate data analysis with wide-spread applications. This paper investigates the possible use of different notions of data depth in non-parametric discriminant analysis. First, we consider the situation where the prior probabilities of the competing populations are all equal and investigate classifiers that assign an observation to the population with respect to which it has the maximum location depth. We propose a different depth-based classification technique for unequal prior problems, which is also useful for equal prior cases, especially when the populations have different scatters and shapes. We use some simulated data sets as well as some benchmark real examples to evaluate the performance of these depth-based classifiers. Large sample behaviour of the misclassification rates of these depth-based non-parametric classifiers have been derived under appropriate regularity conditions.

Keywords: Bayes risk; cross-validation; data depth; elliptic symmetry; kernel density estimation; location shift model; Mahalanobis distance; misclassification rate; Vapnik Chervonenkis dimension

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-9469.2005.00423.x

Affiliations: 1: Institute of Statistical Science 2: Theoretical Statistics and Mathematics Unit, Indian Statistical Institute

Publication date: 2005-06-01