Elliptically Contoured Models in Statistics

Gupta, Arjun K.; Varga, T.

doi:10.1007/978-94-011-1646-6

Cited by 180 publications

(168 citation statements)

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“…This class of distributions is too wide for the construction of optimal tests according to the likelihood ratio criterion. Therefore, other authors (Fang and Zhang (1990), Anderson (1993), Gupta and Varga (1993)) prefer a restricted class of distributions Y with a characteristic function ψ(tr(T T A)) = ψ(tr(T AT )), where A is a p × p positive definite symmetric matrix. The matrices Y of this class have the representation Y = d UA 1/2 with a vectorspherically distributed matrix U (Fang and Zhang (1990), page 96).…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

A note on Left-Spherically Distributed test with covariates

Finos

2011

Statistics & Probability Letters

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“…Consider the multivariate Pearson type II-model (2). Then, under the loss function given by (8), the improved estimator…”

Section: Resultsmentioning

confidence: 99%

“…The following definitions and results presented in this section, and that will be required in the sequel, are taken from Gupta and Varga (1993 …”

Section: Some Preliminariesmentioning

confidence: 99%

Estimation of the precision matrix of multivariate Pearson type II model

Sarr

Gupta

Joarder

2008

Metrika

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In this paper, the problem of estimating the precision matrix of a multivariate Pearson type II-model is considered. A new class of estimators is proposed. Moreover, the risk functions of the usual and the proposed estimators are explicitly derived. It is shown that the proposed estimator dominates the MLE and the unbiased estimator, under the quadratic loss function. A simulation study is carried out and confirms these results. Improved estimator of tr(Σ −1 ) is also obtained.

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“…A context of application is the multivariate general linear model Y = Xθ + E under the assumption that E(n × m) contains n independent and identically distributed spherically symmetric m-vectors. For a unified theoretical treatment of characterizations, properties, and inference for random vectors and matrices with elliptically contoured distributions, see Gupta and Varga [28]. Certain asymmetric distributions closely related to the spherical or elliptically symmetric types have been formulated by multiplying a normal, t-, or other density by a suitable skewing factor.…”

Section: Elliptical Symmetrymentioning

confidence: 99%