Multivariate tests based on left-spherically distributed linear scores

Läuter, Jürgen; Glimm, Ekkehard; Kropf, Siegfried

doi:10.1214/aos/1024691365

Cited by 62 publications

(81 citation statements)

References 12 publications

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“…The two samples case described in application 2 of Läuter et al (1998) fall to be a special case of this generalization.…”

Section: The Lsd Testmentioning

confidence: 99%

“…This is the function lsd.test() in some MTP package available on CRAN. To get the test for the one-sample case of application 1 in Läuter et al (1998) we set X = 1 and no covariates. The R call is as follow: There are many studies evaluating the power of LSD.…”

Section: Software and Simulationmentioning

confidence: 99%

“…The notation A 1/2 indicates the positive definite symmetric matrix that satisfies (A 1/2 ) 2 = A. Under these assumptions Läuter et al (1998) prove the following theorem:…”

Section: Introductionmentioning

confidence: 99%

“…In this brief manuscript we make the Left-Spherically Distributed linear scores test (LSD) of Läuter et al (1998) easier to deal with covariates not under test. The LSD test is a method for multivariate testing also applicable to the p >> n (much more variables than observations).…”

Section: Introductionmentioning

confidence: 99%

“…The following is the theoretical framework used in Läuter et al (1998) (with slight notational changes). The presented theory refers to n × p left-spherically distributed matrices Y (n refers to observations and p to variables).…”

Section: Introductionmentioning

confidence: 99%

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A note on Left-Spherically Distributed test with covariates

Finos

2011

Statistics & Probability Letters

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In this note we extend the Left-Spherically Distributed linear scores test (LSD) of Läuter, Glimm and Kropf test (1998, The Annals of Statistics). The LSD test is a method for multivariate testing also applicable to the p >> n (much more variables than observations). As a key feature, the score coefficients are chosen such that a left-spherical distribution of the scores is reached under the null hypothesis. Here the test is extended to account for nuisance parameters, particularly for covariates that are assumed to explain (part of) the response variables but are not under test. Moreover it is shown how to deal with the random matrix D which is a Borel function of the residuals under the tested null hypothesis instead of a Borel function of total residuals. This provides a D matrix -and a test as well -which is more focused on the effects of the predictors under test. A R code is available on the someMTP package in CRAN.

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“…The two samples case described in application 2 of Läuter et al (1998) fall to be a special case of this generalization.…”

Section: The Lsd Testmentioning

confidence: 99%

Section: Software and Simulationmentioning

confidence: 99%

“…The notation A 1/2 indicates the positive definite symmetric matrix that satisfies (A 1/2 ) 2 = A. Under these assumptions Läuter et al (1998) prove the following theorem:…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A note on Left-Spherically Distributed test with covariates

Finos

2011

Statistics & Probability Letters

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Elliptically Contoured Distributions

Fang

2005

Encyclopedia of Statistical Sciences

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The elliptically contoured distribution (ECD for short) is a class of multivariate distributions that are considered as an extension of the multivariate normal distributions. In this entry, we introduce a historical perspective, basic properties, and subclasses of the ECD. The estimation of parameters of an ECD implies the study of elliptical matrix distributions. A brief review on elliptical matrix distributions is given. Some applications of ECD are discussed.

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Some Applications of Läuter's Technique in Tests for Spherical Symmetry

Liang

Fang

2000

Biom. J.

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Multivariate tests based on left-spherically distributed linear scores

Cited by 62 publications

References 12 publications

A note on Left-Spherically Distributed test with covariates

A note on Left-Spherically Distributed test with covariates

Elliptically Contoured Distributions

Some Applications of Läuter's Technique in Tests for Spherical Symmetry

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