Linear near-neighbor classifiers for correlated categories
Jay L. Devore · Communications in Statistics · 1975
We consider a classification problem in which theta; = θ 1, θ2, . . . is a sequence of unknown categories, with each θ1=0 or 1, and X = X1:, X2:,......is a sequence of observed random variables. The conditional distribution of 1 given θ 1 is assumed normal with variance 1 and mean 29i - 1. We assume that the θ sequence is a realitation of a two-state stationary Markov chain. Thus there is information about θ 1contained not only in X 1 but in all other Xi's. Here we study various proporties of classification rules for θ 1, based on linear functions of the X 1's |j−i| small. When the values of the Markovian parameters are unspecified, it is natural to consider using a plyg-in rule based on substitution of parameter estimates. The large sample behavior of parameter estimates and plug-in rules is iinvestigated, with particular attention to the probability that the plug-in rule yields a smaller risk than the usual minimax procedure appropriate for uncorrelated categories.