# 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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### how to get total Fisher matrix that makes cross synthesis of 2 Fisher matrix

I have initially posted on physics.stackexchange but I think my issue is more adapted on Cross-Validated (so I am going to delete the initial post on physics.stackexchange). I have 2 Fisher matrixes ...
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### Generating correlated positive random numbers (given means, variances and degree of correlation)? [closed]

I have a vector of means and a covariance matrix and I'm trying to create a data set that would like to generate strictly positive numbers that would fit the parameters. I have seen quite a few ...
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### What is the difference between a factorial analysis for mixed data (FAMD) and a PCA on a dataset where qualitative variable are dummy-encoded?

There are many variants of the principal component analysis (PCA) framework for discrete variables or a mixture of quantitative and discrete variables. Image from this book. However, I am not ...
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### Why can't we accurately compute covariance matrix in high dimensions?

I am reading pg 651 of Elements of Statistical Learning,where is says: "The simplest form of regularization assumes that the features are independent within each class, that is, the within-class ...
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### Examples of positive definite periodic covariance matrices

My aim is to find a few examples of positive definite covariance matrices $\pmb{R} = \{R(s,t)\}_{s,t=1}^n$ that satisfy $$R(s,t) = R(s+T, t+T),~~~1\leq s,t \leq n-T,$$ where $T$, $1\leq T\leq n-1$, is ...
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### Combine Two Covariance Matrix [duplicate]

I have two sets of data and each data set has its own mean, standard deviation, and covariance matrix. Can I combine the covariance matrices from each data set to make the covariance matrix for the ...
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### Question relating to joint PDFs

Here are my questions: Let $X$ ~ Unif$(0, 1)$, and $0<a<b<1$. Also, let \begin{cases} Y = 1 & \text{if $0<X<b$} \\ ...
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### A linear process $x_{t}$ satisfies $\sum\limits_{j \in \mathbb Z}\lvert \gamma(j) \rvert < \infty$

A linear process $x_{t}$ is the weighted sum of white noise variates $(w_{t})_{t}$, i.e. $$x_{t}=\mu+\sum\limits_{k \in \mathbb Z}\psi_{k}w_{t-k}$$ such that  \sum\limits_{j \in \mathbb Z}\lvert \...
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### Interpretation of covariance term in loss function

We have an $N\times 1$ vector containing some experimental values $y$, an $N\times 1$ vector $\hat{y}$ containing some predicted values, and an $N\times N$ covariance matrix $V_y$ for the experimental ...
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### Rank of sample covariance matrix when $p = n$

Suppose we have a $p$-dimensional Gaussian distribution, and we take $n$ observations from that distribution. This answer states that when $p > n$, then the sample variance covariance matrix is ...
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### generation of random covariane matrix

in the latest book by Marcos Lopez de Prado, he provides sample code for generating a random variance-covariance matrix. He starts by generating a rectangular dataset with fewer observations than ...
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### Covariance matrices with exponential time decay

I am applying exponential time decay to financial time series to estimate their covariance matrices. The decay factor corresponds to a half-life equal to half of the estimation period. What I get is ...
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### How can a covariance matrix for a normal distribution not be quadratic?

Currently Im reading this paper and in section 3.3., I came across the definition of a multi-dimensional standard normal distribution: \begin{align} q(\pmb{\epsilon}) = \mathcal{N}(\textbf{0}, \...
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### Shouldn't all values of the covariance matrix under homoskedacity be zero?

The following is an excerpt from Greene's Econometric Analysis, 8th Edition. In homoskedacity, the covariance matrix has zero values for the expected errors of all pairs of observations $(i,e)$ ...
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### How can one derive the original data from the correlation- or covariance matrix of that data?

How can one derive the original data from the correlation- or covariance matrix of that data? I know the way a new, reduced dataset can be calculated from the correlationmatrix and it’s eigenvectors ...
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### Is the covariance matrix almost always postive definite?

I understand a covariance matrix is always positive semi-definite, but it seems that the covariance matrix would almost always be positive definite (although theoretically is only guaranteed to be ...
I have a data set of $N$ points to which I have fit an equation of $n$ parameters $\theta_{1..n}$ such that $y_i \sim f(x_i; \theta_{1..n})$. These data $(x_{1..N},y_{1..N})$ have been provided with ...
### Finding a matrix $\mathbf{A}$ that projects a point to an eigenvector of $\mathbf{A}\mathbf{C}\mathbf{A}^T$
Suppose $\mathbf{b}=[b_1,b_2]'$ is $2\times 1$ and $\mathbf{C}$ is a full-rank symmetric $2\times 2$ matrix which both are real and given. Now, consider the problem of finding a $2\times 2$ matrix \$\...