# Questions tagged [multivariate-statistical-analysis]

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### CDF and PDF of dependent variables originating from a real life shock models

Suppose there are two sources of shocks and a system with two components. Shock A can affect the first component and Shock B can affect both the components. I am trying to find the joint distribution ...
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1 vote
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### Vine Copulas: Conditional Copula cdf in higher dimensions

Hello :) I am currently working on a project where I am stuck calculating the following term: $u_{i(e)|D(e)} = C_{i(e)|D(e)}(u_{i(e)}|D(e))$ $u_{j(e)|D(e)} = C_{i(e)|D(e)}(j_{i(e)}|D(e))$ The ...
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### Obtaining multivariate linear regression coefficients from residual values of simple linear regressions

We are interested in a multivariate linear regression of $Y$ against $X_1$ and $X_2$. More specifically we want to know the regression coefficients of $X_1$. There is a sample drawn of size $n$, but ...
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### Kullback–Leibler divergence of two multivariate normal distribution

I have a problem: I want to calculate Kullback-Leibler (KL) divergence of two dataset where $X_{1}$ has $M$ features with its multivariate normal distribution $\mathcal{N}(\mu_1, \sigma_1)$ and $X_{2}$...
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### Work someone check my work using Bayes Classifier?

Background: Suppose we have two classes for p=2 variate observations, where the probability for class 1 follows MVN($\mu_1$, $\Sigma$) and the population for class 2 follows MVN($\mu_2$, $\Sigma$) ...
• 347
1 vote
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### Transform Wishart distribution to Chi-square distribution

This's actually what I'm trying to prove: $$\frac {a^{'}\Sigma^{-1}a}{a^{'}W^{-1}a} \sim \chi^{2}_{n-p+1}$$ $a$ is any P-dimensional nonzero constant vector, and $W \sim W_{p}(n,\Sigma)$, $\Sigma$ ...
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### How to solve the matrix equation $\sum_iA_i^TA_iXB_iB_i^T=\sum_iA_i^TC_iB_i^T$ efficiently?

How would I go about solving the matrix equation $\sum_iA_i^TA_iXB_iB_i^T=\sum_iA_i^TC_iB_i^T$ for $X$? The simplest thing to do would be to, of course, consider $Y=\sum_iA_i^TC_iB_i^T$, vectorise and ...
1 vote
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### Modeling angles and magnitudes using a bi-variate gaussian.

I have a bunch of points in n-d space who's coordinates follow a Normal distribution $(X=x_1,x_2,...,x_n\sim N(0,1) )$. The coordinates form an angle $\theta$ (with respect to some arbitrary vector $V$...
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Suppose I have a $p \times n$ (with $p \geq n$) matrix $\bf U$ such that ${\bf U}' {\bf U} = {\bf I}_{n}$ and that $\bf U$ is uniformly distributed on the Stiefel manifold $V_{n,p}$. I would like to ...