Asymptotic Analysis of the Nearest Neighbor Decision Rule

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Department of Electrical Engineering, Stanford University., 1966 - Statistical decision - 65 pages
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The nearest-neighbor decision rule (NN rule) assigns to an unclassified sample the classification of the nearest of n previously classified samples. In a large sample analysis it is shown, under very weak regularity conditions, that the risk incurred by this nonparametric rule is less than twice the Bayes risk. A variety of standard decision problems are treated, and in some cases the bounds given on the NN risk are the best possible. The natural extension of the NN rule to the decision rule that considers several nearby neighbors and takes a vote is also treated. Consideration is given to some of the implementation problems arising in connection with the NN rule. In particular, a method of optical computation is suggested to carry out the necessary calculations and a performance-feedback technique is proposed to determine sample-size requirements. (Author).

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Contents

INTRODUCTION
1
EXTENSION AND RELATED ANALYSIS
26
PRACTICAL CONSIDERATIONS
47

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