Journal Article10.1007/S00362-016-0766-7
Multinomial interpoint distances
Reza Modarres
- 01 Mar 2018
- Vol. 59, Iss: 1, pp 341-360
9
TL;DR: The properties of the squared Euclidean interpoint distances (IDs) drawn from multinomial distributions are explored and applications of IDs for testing goodness of fit, the equality of high dimensional mult inomial distributions, classification and outliers detection are discussed.
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Abstract: We explore the properties of the squared Euclidean interpoint distances (IDs) drawn from multinomial distributions. We consider the distances within one sample and across two samples and obtain their means, variances, covariances and distributions. We discuss applications of IDs for testing goodness of fit, the equality of high dimensional multinomial distributions, classification, and outliers detection. A simulation study compares the performance of the $$\chi ^2$$
and the likelihood ratio statistics for testing equality of distributions, with methods based on the IDs.
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