# Tagged Questions

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### How to extract covariance (error) matrix of independent parameters x,y from covariance matrix of dependent parameters x,y,z?

Suppose I have a covariance (error) matrix C_xyz for system with 3 parameters: x, y, z. Then it appears that ...
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### What does the inverse of covariance matrix says about data? (Intuitively)

I'm curious about the nature of $\Sigma^{-1}$. Can anybody tell something intuitive about "What does $\Sigma^{-1}$ say about data?"
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### Covariance matrix equality

The (unbiased) sample covariance matrix $$\mathbf{S}=\dfrac{1}{n-1}\sum_{j=1}^{n}(\mathbf{X}_{j}-\bar{\mathbf{X}})(\mathbf{X}_{j}-\bar{\mathbf{X}})^{T}$$ can be rewritten as ...
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### Priors on matrix determinant

I have a positive semi definite matrix (covariance matrix). Was wondering are there any distributions that can place a prior on the determinant? Something along lines of $$\exp(-k|X|)$$ Note that ...
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### Factor Analysis…Covariance Matrix help

I'm trying to run a factor analysis in SPSS on a set of social vulnerability data for my thesis. I have 5 communities, with 26 social vulnerability variables for each community. My overall aim is to ...
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### Whitening a dataset with fewer observations than variables

I have a k x n dataset where k equals the number of variables and n equals the number of observations per variable. I know these data are correlated and I would like to whiten them with the ordinary ...
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### Multivariate EWMA covariance estimation?

I want to calculate the VaR of my portfolio consisting of 4 assets with the following formula: $VaR_t=\sqrt{w^T\Sigma_tw}z_\alpha$ So for each time point I need to calculate the covariance matrix. ...
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### What happens to the covariance matrix when the errors are independent?

I was wondering, what happens to the covariance matrix of the errors, when I assume that all the errors are stochastically independent? Is the covariance matrix still: \sigma^2I = ...
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### Is every covariance matrix positive definite?

I guess the answer should be yes, but I still feel something is not right. There should be some general results in the literature, could anyone help me?
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### Covariance matrix explanation

I try to understand and visualize myself covariance matrix. Supposing I have a matrix A = [ 2 3 4; 5 5 6 ], how do I calculate its covariance matrix, and what is ...
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### Variance Covariance matrix of regression coefficients

In a procedure, I am resampling (bootstrapping) from a Y vector and X matrix. For each resample, I standardize. Then I run a linear model, and obtain the regression coefficients for each variable of ...
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### Why are the eigenvalues of a covariance matrix corresponding to the data's variance? [duplicate]

For multi-dimensional data, we can compute its covariance matrix, and then the eigenvalues and eigenvectors. It turns out that the eigenvector with the largest eigenvalue corresonds to the direction ...
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### Problem when creating matrix of values based on covariance matrix

I want to simulate a data set with similar covariance structure as my observed data (which is a SNP by gene p-value matrix, dim ~600k*8368), and have calculated a covariance matrix (dimensions ...
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### Covariance matrix in R with non-numeric variables

I am modeling a Gaussian distribution for a computational biology application, and I am working in the statistical package "R". In this regard, my problem is that I have to construct a covariance ...
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### Problem with singular covariance matrices when doing Gaussian process regression

I'm working with Gaussian process regression. Currently I start testing different covariance functions and compositions to see what type of data they could describe best. I made an own implementation ...
Working with the generalized covariance formula for vector, $x$, I have: $E[(x-\mu)(x-\mu)^T)] = E(xx^t) - \mu E(x^T)$ But the term $E(x^T)$ doesn't make much sense to me. Does anyone have an idea ...