# Questions tagged [covariance-matrix]

A $k\times k$ matrix of covariances between all pairs of $k$ random variables. It is also called variance-covariance matrix or simply the covariance matrix.

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### Creating a Covariance Matrix

Lets say that you have the correlation of x,y and you have the standard deviations of x and y , how would you then find the covariance of x,y using the correlation of x,y and and the standard ...
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### How to transform the covariance matrix for a GHK simulator?

I've used an MCMC Gibbs sampler to estimate parameters of the Multinomial Probit Model. In doing so, I've differenced all utilities with respect to the last alternative, such that I obtained (J-1) ...
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### How $\Sigma = AA^T$ derives to $A = \Sigma^{1/2}$ [closed]

This is how I start, but I'm stuck on how to proceed. I think I'm missing some algebra properties. $\Sigma=AA^T$ $\Sigma^{-1} = (AA^T)^{-1}$
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### Generate Multivariate Log-Normal Variables with given Covariance and Mean

Let ${\bf X}=(X_1,...,X_n)$ be an $n$-dimensional log-normal random variable. I want to $force$ my random variables to be such that $Cov(X_i,X_j)=\Sigma_{i,j}$ and $E(X_i)=\mu_i$ where $\Sigma_{i,j}$ ...
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### Unbiasedness and Variance of Predictions

Here is the problem I'm working on: I'm not quite sure if I'm showing either unbiasedness property right, and am stuck on finding the expressions for the variances. Here's what I've done so far. (a) ...
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### Properties of Covariance (Matrix and Vector Case)

In 1 dimensional case, we have $Cov(cX_1,X_1) = cCov(X_1,X_1).$ Here $X_1$ is just a random variable. I was wondering if we have an analogue for $Cov(AX_1,X_1)$, where $A$ is a matrix with ...
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### How do I construct a variance-covariance matrix from a matrix formulation of a MLR? [duplicate]

I'm trying to calculate the SE for each coefficient given by a matrix formulation of MLR by the root of each diagonal in the so-called variance-covariance matrix, but I'm unsure how to construct this ...
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### Mahalanobis distance - understanding the formula [duplicate]

I've read quite a few explanations on this topic, liking this one the most: https://mccormickml.com/2014/07/22/mahalanobis-distance/ But there is still one thing I don't understand. I understand ...
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### Distribution of the squared norm of a vector with multivariate normal distribution and dependent components [duplicate]

Let x be a p-dimensional random vector with dependent components. Assume that x is distributed according to a multivariate normal distribution with mean vector m and variance/covariance matrix V which ...
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### Why the first principal component is mostly negative while the second component is mostly positive?

I am running PCA for a fleet management data frame $X$, where each column is a city, each row is a date, there are 50 cities and 500 dates. I run PCA on $A=X^{T}X$. Then the first component $v_{1}$ ...
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### How to use inverse information matrix and Delta method to find sample variation?

Explain how the inverse of the information matrix and the Delta Rule be used to generate an approximate sampling variance for the estimated proportion exp(beta 0 + beta 1)/(1+exp( beta 0 + beta 1))? ...
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### CFA, Covariance matrix is not positive definite?

I have a 3-factor CFA model with 16 items. I conducted 8 groups comparison.For one group, Amos analytic result showed " The following covariance matrix is not positive definite." The sample size for ...
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### How to create a variance-covariance matrix for forecasted fantasy basketball scores?

I have three basketball players who have played in games together and I want to find a Variance-Covariance matrix that will be as accurate as possible for their fantasy points in an upcoming game. My ...
I am basically estimating the shape of an unknown function f(x) from multi-dimensional chemical reaction data by estimating the most likely function values $f$ on a grid $x$ with kernel regression. To ...