Effect of random errors on generalized distance computations

摘要

There is growing interest in devising non-statistical classification algorithms for multivariate populations. Statistical algorithms are not appropriate if an adequate statistical model for the population does not exist. Such algorithms may be sensitive (unstable) to errors in their data. The particular case of populations of objects characterized by binary attributes susceptible to independent and equiprobable errors is examined. The determination of stability requires the prior computation of the expectation of a statistical function of the object-pair similarities. The order and convergence of a numerical approxiamation for determining these expectation with prescribed accuracy is examined in the sub-asymptotic case in which normality does not occur.