# Questions tagged [multivariate-normal-distribution]

The multivariate normal distribution, is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. (Also called, multivariate Gaussian)

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### How can I quantify uncertainty for a least squares estimator in a multivariate linear regression with covariance structure?

Suppose that we have $$\mathbf{y}\sim\text{N}(\mathbf{X}\boldsymbol{\beta},\sigma^2\mathbf{M}\mathbf{M}'),$$ and let $\boldsymbol{\hat{\beta}}$ be the least squares estimator for $\boldsymbol{\beta}$. ...
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### Using linear combination of multivariate normal $X$

I have a question and its answer but I don't understand it. would you please explain it to me? QUESTION: Let $X$ follow a $N(0, 1)$ and $Z$ a random variable independent of $X$ following a $U(-1, 1)$. ...
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### MLE of multivariate normal distribution when the VCV matrix is full of equations

Short Version: Given a variance covariance matrix for my multivariate normal distribution where the entries are equations of other parameters, how do I find which of those parameter values maximizes ...
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### How to Handle Non-Multinormality in the Context of Exploratory Factor Analysis for Logistic Regression

I'm trying to follow the book A Step-by-Step Guide to Exploratory Factor Analysis with R and Rstudio, by Marley W. Watkins, and apply the principles in the book to a real-world data set. Ultimately, ...
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### meaning of empirical argument in mvrnorm

I'm using the mvrnorm function from MASS library, and I have a question regarding the ...
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### Is this the formula for the conditional covariance of normally distributed random variables? [duplicate]

Assuming $X$, $Y$, and $Z$ are normally distributed random variables, is it true that: $Cov[X, Y | Z] = Cov[X, Y] - Cov[X, Z]Cov[Y, Z] / Var[Z]$ Could you provide a simple derivation?
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### corr(xz, yz) given all pairwise correlations

Suppose we have random variables $x,y,z$ where each random variable has mean 0 and standard deviation of 1. $Corr(x,y) = a$, $corr(x,z)=b$ and $corr(y,z)=c$ How do I go about calculating $corr(xz, yz)$...
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### Combining factors, represented as normal distributions, to one combined factor, normally distributed

I'm trying to combine the different factors that may affect running pace, such as GPS-measured distance, grade, terrain, heat and other factors (such as wind etc.). Each factor is represented as a ...
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### Using Copulas to find mutual information

I have two multidimensional datasets $X, Y$ of dimensions $m \times n$. Here $m$ is the successive measurements and $n$ is the data collected during each measurement. We can say each of $m$ are ...
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