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Certain nonparametric classification rules and their asymptotic efficiencies
Author(s) -
Govindarajulu Z.,
Gupta A. K.
Publication year - 1977
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314775
Subject(s) - nonparametric statistics , mathematics , consistency (knowledge bases) , parametric statistics , statistics , location parameter , scale (ratio) , class (philosophy) , property (philosophy) , asymptotic distribution , probability distribution , discrete mathematics , artificial intelligence , computer science , estimator , geography , philosophy , cartography , epistemology
Abstract Two nonparametric classification rules for e‐univariace populations are proposed, one in which the probability of correct classification is a specified number and the other in which one has to evaluate the probability of correct classification. In each case the classification is with respect to the Chernoff and Savage (1958) class of statistics, with possible specialization to populations having different location shifts and different changes of scale. An optimum property, namely the consistency of the classification procedure, is established for the second rule, when the distributions are either fixed or “near” in the Pitman sense and are tending to a common distribution at a specified rate. A measure of asymptotic efficiency is defined for the second rule and its asymptotic efficiency based on the Chernoff‐Savage class of statistics relative to the parametric competitors ie the case of location shifts and scale changes is shown to be equal to the analogous Pitman efficiency.