Questions tagged [wishart]

The Wishart distribution is a common matrix distribution on square symmetric semi-definite matrices.

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Distribution of inverse Wishart to a power?

In a related question, I had asked about the norm induced by an inverse Wishart matrix. I am interested in generalizing that result somewhat. Let $A\sim\mathcal{W}_p\left(I,n\right)$, a Wishart matrix ...
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Entropy of Inverse-Wishart distribution

What is the entropy of the Inverse-Wishart distribution? I need just a reference, but derivation (e.g. using inverse property) would be interesting too.
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Sampling distribution of average of some covariance matrices

I have $K$ datasets, each with $N$ variables and $M$ samples (they are in fact EEG time series, but I discard time and treat them as $K$ iid multivariate samples) and assume they are coming from the ...
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Expected eigenvalues of a Wishart Matrix

I consider a $n\times n$ Wishart Matrix with expected value $p \cdot I_n$, i.e. a matrix of the form $$W = XX'$$ with $X$ a $n\times p$ matrix with independent standard normal entries. It is easy ...
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If $X$ has a Wishart distribution $W_p(n,\Sigma)$ , what's the distribution for $cX$ where $c>0$ ? I know that for a $\chi^2_n (x)$ distribution with $n$ degrees of freedom, $c\chi^2$ follows $\... 0answers 203 views Expectation of the inverse of$\textbf{z} \textbf{z}^{H}$where$\textbf{z}$is a complex Gaussian vector Considering the vector$\textbf{z} \sim \mathcal{CN}(\textbf{0}_{M},\Theta_{M \times M})$, what would be the expectation of$\frac{1}{\textbf{z} \textbf{z}^{H}}$, i.e.,$\mathbb{E} \left\lbrace \frac{...
I am solving the next exercise about a property of a Wishart Distribution: $$M_1\sim W_p(\Sigma,n_1)$$ $$M_2\sim W_p(\Sigma,n_2)$$ are independent, then $M_1+M_2\sim W_p(\Sigma,n_1+n_2)$ I have ...