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AN ASYMPTOTIC EXPANSION OF THE EXPECTATION OF THE ESTIMATED ERROR RATE IN DISCRIMINANT ANALYSIS 1
Author(s) -
Mclachlan G. J.
Publication year - 1973
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1973.tb00201.x
Subject(s) - mahalanobis distance , mathematics , discriminant function analysis , monte carlo method , statistics , discriminant , asymptotic expansion , function (biology) , asymptotic analysis , word error rate , mathematical analysis , computer science , artificial intelligence , biology , evolutionary biology
Summary When a sample discriminant function is computed, it is desired to estimate the error rate using this function. This is often done by computing G (‐ D /2), where G is the cumulative normal distribution and D 2 is the estimated Mahalanobis' distance. In this paper an asymptotic expansion of the expectation of G (‐ D /2) is derived and is compared with existing Monte Carlo estimates. The asymptotic bias of G (‐ D /2) is derived also and the well‐known practical result that G (‐ D /2) gives too favourable an estimate of the true error rate