Search results for "Quadrant test"

showing 2 items of 2 documents

Sign test of independence between two random vectors

2003

A new affine invariant extension of the quadrant test statistic Blomqvist (Ann. Math. Statist. 21 (1950) 593) based on spatial signs is proposed for testing the hypothesis of independence. In the elliptic case, the new test statistic is asymptotically equivalent to the interdirection test by Gieser and Randles (J. Amer. Statist. Assoc. 92 (1997) 561) but is easier to compute in practice. Limiting Pitman efficiencies and simulations are used to compare the test to the classical Wilks’ test. peerReviewed

Statistics and ProbabilityDiscrete mathematicsStatistics::TheoryMultivariate random variableExtension (predicate logic)robustnessQuadrant testPitman efficiencyTest (assessment)Exact testStatisticsChi-square testTest statisticSign testaffine invarianceStatistics Probability and UncertaintyIndependence (probability theory)MathematicsWilks’ test
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Multivariate nonparametric tests of independence

2005

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 …

Statistics and ProbabilityMultivariate statisticsMultivariate analysisNonparametric statisticsAsymptotic distributionMultivariate normal distributionSpearman's rank correlation coefficientQuadrant testriippumattomuusPitman efficiencyKendall's tauStatisticsHigh-dimensional statisticsaffine invarianceStatistics Probability and UncertaintySpearman's rhoRobustnessMathematicsStatistical hypothesis testing
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