Book ChapterDOI
The Asymptotic Distribution of Characteristic Roots and Vectors in Multivariate Components of Variance
T. W. Anderson
- pp 177-196
TLDR
In this paper, the asymptotic distribution of the characteristic roots and vectors of one Wishart matrix in the metric of another as the two degrees of freedom increase in fixed proportion is obtained.Abstract:
The asymptotic distribution of the characteristic roots and vectors of one Wishart matrix in the metric of another as the two degrees of freedom increase in fixed proportion is obtained. In the balanced one-way multivariate analysis of variance these two matrices are the sample effect and error covariance matrices, and the numbers of degrees of freedom are (approximately) proportional to the number of classes. The maximum likelihood estimate of the effect covariance matrix of a given rank depends on the characteristic roots and vectors.read more
Citations
More filters
Journal ArticleDOI
On wielandt's inequality and its application to the asymptotic distribution of the eigenvalues of a random symmetric matrix
Morris L. Eaton,David E. Tyler +1 more
TL;DR: In this article, a relatively obscure eigenvalue inequality due to Wielandt is used to give a simple derivation of the asymptotic distribution of the eigenvalues of a random symmetric matrix.
A bibliography on variance components an introduction and an update: 1984-2002
Hardeo Sahai,Anwer Khurshid +1 more
TL;DR: In particular, the study of variance through a class of linear models known as random and mixed models is a central topic in statistics with wide ramifications in both theory and applications as discussed by the authors.
Journal ArticleDOI
Asymptotic properties of eigenmatrices of a large sample covariance matrix
TL;DR: This result provides further evidence in support of the conjecture that the distribution of the eigenmatrix of $S_n$ is asymptotically close to that of a Haar-distributed unitary matrix.
Sphering and its properties
Guoying Li,Jian Zhang,Academia S +2 more
TL;DR: In this paper, the authors discuss properties of sphering procedures, such as affine equivariance/invariance, application to projection pursuit (PP) and asymptotic behavior.
Journal ArticleDOI
Testing dimensionality in the multivariate analysis of variance
T. W. Anderson,Yasuo Amemiya +1 more
TL;DR: In this article, the problem of testing the dimension of the effect space is treated, and the test statistic is shown to have the same asymptotic null distribution as that for the balanced random effect model.
References
More filters
Book
An Introduction to Multivariate Statistical Analysis
TL;DR: In this article, the distribution of the Mean Vector and the Covariance Matrix and the Generalized T2-Statistic is analyzed. But the distribution is not shown to be independent of sets of Variates.
Journal ArticleDOI
Introduction to Multivariate Statistical Analysis.
William G. Madow,T. W. Anderson +1 more
Book
Measurement Error Models
TL;DR: In this paper, the authors provide a complete treatment of an important and frequently ignored topic, namely measurement error models, including regression models with errors in the variables, latent variable models, and factor models.
Journal ArticleDOI
Asymptotic theory for principal component analysis
TL;DR: In this paper, the asymptotic distribution of the characteristic roots and vectors of a sample covariance matrix is given when the observations are from a multivariate normal distribution whose covariance matrices has characteristic roots of arbitrary multiplicity.
Related Papers (5)
Asymptotic distributions of likelihood ratio criteria for testing latent roots and latent vectors of a covariance matrix under an elliptical population
Takeshi Hayakawa,Madan L. Puri +1 more