3
$\begingroup$

I'm trying to figure out if Wishart can be close to Normal for a number of degrees of freedom enough large.

About chi-squared distribution, Wikipedia states:

By the central limit theorem, because the chi-squared distribution is the sum of k 
independent random variables with finite mean and variance, it converges to a normal 
distribution for large k. For many practical purposes, for k > 50 the distribution is 
sufficiently close to a normal distribution for the difference to be ignored.

Since Wishart is presented as a generalization to multiple dimensions of the chi-squared distribution, is there a similar property?

$\endgroup$
1
$\begingroup$

The Wishart distribution (when dimension is 2 or higher) is a distribution on a space of matrices, if the underlying space had dimension $d$, the space of symmetric positive matrices $d \times d$ has dimension $d(d+1)/2$, so for approximating Wishart by a normal you would need a normal of that dimension which in addition fulfills the (non-linear) conditions necessary to be a positive definite matrix. That doesn't sound like being possible, so I believe the answer to your question is NO.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.