Distribution-free partial discrimination procedures

AbstractThis paper reviews discrimination procedures which provide distribution-free control over the individual misclassification probabilities. Particular emphasis is placed on the two-population rank method developed by Broffitt, Randles and Hogg, which utilizes the general formulation of Quesenberry and Gessaman. It is shown that the rank method extends from two to three or more populations in a natural and flexible fashion. A Monte Carlo study compares two suggested extensions with others proposed by Broffitt

A method for resolving ties in asymptotic relative efficiency

This article presents a method for determining which of two tests may offer an advantage in power when their asymptotic relative efficiencies (ARE) are the same. The method maintains some of the desirable properties of ARE, such as ease of calculation and singular result based upon asymptotic properties of the tests. However, using higher-order Taylor expansions of the test statistics' means, the procedure offers additional insight into the finite sample size behavior of the tests. Two examples demonstrate the method.Asymptotic relative efficiency ARE Power analysis Asymptotic deficiency Nonparametric statistics

On zeroes in sign and signed rank tests

When zeroes (or ties within pairs) occur in data being analyzed with a sign test or a signed rank test, nonparametric methods textbooks and software consistently recommend that the zeroes be deleted and the data analyzed as though zeroes did not exist. This advice is not consistent with the objectives of the majority of applications. In most settings a better approach would be to view the tests as testing hypotheses about a population median. There are relatively simple p-values available that are consistent with this viewpoint of the tests. These methods produce tests with good properties for testing a different (often more appropriate) set of hypotheses than those addressed by tests that delete the zeroes

Multivariate nonparametric tests of independence

New test statistics are proposed for testing whether two random vectors are independent. Gieser and Randles, as well as Taskinen, Kankainen, and Oja have introduced and discussed multivariate extensions of the quadrant test of Blomqvist. This article serves as a sequel to this work and presents new multivariate extensions of Kendall's tau and Spearman's rho statistics. Two different approaches are discussed. First, interdirection proportions are used to estimate the cosines of angles between centered observation vectors and between differences of observation vectors. Second, covariances between affine-equivariant multivariate signs and ranks are used. The test statistics arising from these two approaches appear to be asymptotically equivalent if each vector is elliptically symmetric. The spatial sign versions are easy to compute for data in common dimensions, and they provide practical, robust alternatives to normal-theory methods. Asymptotic theory is developed to approximate the finite-sample null distributions as well, as to calculate limiting Pitman efficiencies. Small-sample null permutation distributions are also described. A simple simulation study is used to compare the proposed tests with the classical Wilks test. Finally, the theory is illustrated by an example.peerReviewe