Invariant scale matrix hypothesis tests under elliptical symmetry

Chmielewski, Margaret A.

doi:10.1016/0047-259x(80)90054-8

Cited by 31 publications

(5 citation statements)

References 15 publications

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“…These normal theory methods can, however, be sensitive to deviations from normality and, in particular, to the kurtosis of data distributions. Multivariate distributions that are convenient for investigating the sensitivity of normal theory methods to kurtosis are the elliptical distributions (Chmielewski 1981;Devlin, Gnanadesikan, and Kettenring 1976;Muirhead 1982, sec. 1.5).…”

Section: Introductionmentioning

confidence: 99%

Analysis of Covariance Structures under Elliptical Distributions

Shapiro

Browne

1987

Journal of the American Statistical Association

103

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This article examines the adjustment of normal theory methods for the analysis of covariance structures to make them applicable under the class of elliptical distributions. It is shown that if the model satisfies a mild scale invariance condition and the data have an elliptical distribution, the asymptotic covariance matrix of sample covariances has a structure that results in the retention of many of the asymptotic properties of normal theory methods. If a scale adjustment is applied, the likelihood ratio tests of fit have the usual asymptotic chi-squared distributions. Difference tests retain their property of asymptotic independence, and maximum likelihood estimators retain their relative asymptotic efficiency within the class of estimators based on the sample covariance matrix. An adjustment to the asymptotic covariance matrix of normal theory maximum likelihood estimators for elliptical distributions is provided. This adjustment is particularly simple in models for patterned covariance or correlation matrices. These results apply not only to normal theory maximum likelihood methods but also to a class of minimum discrepancy methods. Similar results also apply when certain robust estimators of the covariance matrix are employed.

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Section: Introductionmentioning

confidence: 99%

Analysis of Covariance Structures under Elliptical Distributions

Shapiro

Browne

1987

Journal of the American Statistical Association

103

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“…3. The distribution of u is elliptically symmetric (see Chmielewski, 1980). 4. å and í are statistically independent.…”

Section: Estimation Of Rcr Models: ®Nite Sample Resultsmentioning

confidence: 99%

Estimated Generalized Least Squares for Random Coefficient Regression Models

Anh¹,

Chelliah²

1999

Scandinavian J Statistics

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This paper considers a general class of random coef®cient regression (RCR) models to represent pooled cross-sectional and time series data. A new method is given to estimate the covariance matrix of the error component in these RCR models. Also, the asymptotic and small sample properties of the estimated generalized least squares estimator of the regression coef®cient vector are established. Procedures for testing a linear restriction on the mean vector of the random coef®cients are derived. Finally, a test for non-randomness in the RCR model is devised, and the asymptotic distribution of the test statistic is obtained.

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“…This definition is more general than others given in the literature in so far as otherauthors take Φ = I n (or Σ = 7 n ), see e.g. Chmieliwski [3].…”

Section: Elliptically Contoured Matrix Variate Distributionsmentioning

confidence: 99%

Multivariate elliptically contoured and ө-generalized normal models

Gupta¹

1998

Random Operators and Stochastic Equations

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Tn this article the main results of the Multivariate elliptically contoured linear models are considered. Multivariate elliptically contoured linear models arise in many areas of application. See the reference given in this paper for some of these applications. Note that applications of Multivariate elliptically contoured linear models are not exhausted by the applications in physics, multivariate statistical analysis, and the theory of nonordered structures. Now, theory of random matrices is also used in the theory of stability of solutions of stochastic systems, in linear stochastic programming, in molecular chemistry and in the theory of experiment disign. This paper is designed for statisticians, mathematicians, physicists, scientists, and engineers of different specialties, who use random matrices and theoretical-probability methods in their work. t=l Jb=lBrought to you by |

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Invariant scale matrix hypothesis tests under elliptical symmetry

Cited by 31 publications

References 15 publications

Analysis of Covariance Structures under Elliptical Distributions

Analysis of Covariance Structures under Elliptical Distributions

Estimated Generalized Least Squares for Random Coefficient Regression Models

Multivariate elliptically contoured and ө-generalized normal models

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