6533b833fe1ef96bd129c3c2

RESEARCH PRODUCT

Affine-invariant rank tests for multivariate independence in independent component models

Sara TaskinenDavy PaindaveineHannu Oja

subject

Statistics and ProbabilityMultivariate statisticssingular information matricesRank (linear algebra)Gaussianuniform local asymptotic02 engineering and technology01 natural sciencesdistribution-free testsCombinatoricstests for multivariate independence010104 statistics & probabilitysymbols.namesakenormaalius0202 electrical engineering electronic engineering information engineeringApplied mathematics0101 mathematicsStatistique mathématiqueIndependence (probability theory)Parametric statisticsMathematicsDistribution-free testsuniform local asymptotic normalityNonparametric statistics020206 networking & telecommunicationsIndependent component analysisrank testsAsymptotically optimal algorithmsymbolsindependent component models62H1562G35Statistics Probability and UncertaintyUniform local asymptotic normality62G10

description

We consider the problem of testing for multivariate independence in independent component (IC) models. Under a symmetry assumption, we develop parametric and nonparametric (signed-rank) tests. Unlike in independent component analysis (ICA), we allow for the singular cases involving more than one Gaussian independent component. The proposed rank tests are based on componentwise signed ranks, à la Puri and Sen. Unlike the Puri and Sen tests, however, our tests (i) are affine-invariant and (ii) are, for adequately chosen scores, locally and asymptotically optimal (in the Le Cam sense) at prespecified densities. Asymptotic local powers and asymptotic relative efficiencies with respect to Wilks’ LRT are derived. Finite-sample properties are investigated through a Monte-Carlo study.

yearjournalcountryeditionlanguage
2016-01-01
http://urn.fi/URN:NBN:fi:jyu-201609073997