scholarly journals Joint Distribution of the Extreme Roots of a Covariance Matrix

1970 ◽  
Vol 41 (2) ◽  
pp. 655-657 ◽  
Author(s):  
T. Sugiyama
Keyword(s):  
Covariance Matrix ◽  
Joint Distribution

scholarly journals On n/p-Asymptotic Distribution Of Vector Of Weighted Traces Of Powers Of Wishart Matrices

2018 ◽  
Vol 33 ◽  
pp. 24-40 ◽  
Author(s):  
Jolanta Pielaszkiewicz ◽  
Dietrich Von Rosen ◽  
Martin Singull
Keyword(s):  
Normal Distribution ◽  
Covariance Matrix ◽  
Asymptotic Distribution ◽  
Joint Distribution ◽  
Recursive Formula ◽  
Multivariate Normal ◽  
Wishart Matrices ◽  
The Matrix ◽  
Matrix Normal ◽  
Matrix Normal Distribution

The joint distribution of standardized traces of $\frac{1}{n}XX'$ and of $\Big(\frac{1}{n}XX'\Big)^2$, where the matrix $X:p\times n$ follows a matrix normal distribution is proved asymptotically to be multivariate normal under condition $\frac{{n}}{p}\overset{n,p\rightarrow\infty}{\rightarrow}c>0$. Proof relies on calculations of asymptotic moments and cumulants obtained using a recursive formula derived in Pielaszkiewicz et al. (2015). The covariance matrix of the underlying vector is explicitely given as a function of $n$ and $p$.

On the ith Latent Root of a Complex Matrix(1)

1972 ◽  
Vol 15 (3) ◽  
pp. 323-327
Author(s):  
Sabri Al-Ani
Keyword(s):  
Statistical Analysis ◽  
Covariance Matrix ◽  
Joint Distribution ◽  
Latent Root ◽  
Multivariate Normal ◽  
Complex Matrix ◽  
Image Position ◽  
Latent Roots

Goodman [1] has pointed out the applications of the distributional results of the complex multivariate normal statistical analysis. Khatri [4], has suggested the maximum latent root statistic for testing the reality of a covariance matrix. The joint distribution of the latent roots under certain null hypotheses can be written as, [2], [3],1whereand

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