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On Maximum Depth and Related Classifiers
Author(s) -
GHOSH ANIL K.,
CHAUDHURI PROBAL
Publication year - 2005
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2005.00423.x
Subject(s) - mathematics , parametric statistics , sample (material) , artificial intelligence , benchmark (surveying) , multivariate statistics , population , linear discriminant analysis , statistics , pattern recognition (psychology) , classifier (uml) , machine learning , computer science , geography , cartography , chemistry , demography , chromatography , sociology
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.