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Re: Multivariate student t: normalization in mvtrnd

From: Iñigo Urteaga
Subject: Re: Multivariate student t: normalization in mvtrnd
Date: Mon, 26 Nov 2012 18:03:40 -0500

Hi Dan,

Thank you for your help. As you suggest, V is the covariance matrix
and that is indeed why in my proposed method:

samples=Sigma' * mvtrnd( eye(n), nu, M)'; (1)

we need to use only Sigma' as given by the Cholesky decomposition
(which can be thought of as the matrix analogue of the square root of
a number).

We can obviously not use Sigma=chol(V) directly into mvtrnd, as this
matrix is not positive definite. Your suggestion of directly using the
square root over the matrix V does not work either, as the provided
sqrt(V) is again factorized by the mvtrnd function if diagonal items
are non-unit. That is, the resulting covariance relates now to:

nu/(nu-2) * sqrt(V)./(sqrt(diag(sqrt(V))*diag(sqrt(V))))

but not to nu/(nu-2) * V nor nu/(nu-2) * sqrt(V)

I am looking forward to figuring this issue out, so I truly appreciate
your suggestion.

Thank you very much,


On Mon, Nov 26, 2012 at 5:44 PM, Daniel J Sebald <address@hidden> wrote:
> is typically a variable associated with standard deviation and sigma^2
> variance.  You've defined V=Sigma * Sigma' which is more along the lines of
> variance, not standard deviation.

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