# 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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### Eigenvalues/Eigenvectors of Correlation and Covariance matrices

Suppose $\Sigma$ is a covariance matrix $P$ is its corresponding correlation matrix. Let $\lambda_1, \dots, \lambda_p$ and $\tau_1, \dots, \tau_p$ denote the ordered eigenvalues of $\Sigma$ and $P$, ...
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### Bessel correction for the variance of dependent sample

Assuming a sample $X_1, X_2, ..., X_n$, the sample variance is calculated as $s^2 = \frac{1}{n-1} \sum (X_i-\bar{X})^2$ The fact that there is $n-1$ in the denominator instead of $n$ is called the ...
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### Existence of stationary process with a given ACF

Consider the sequence $$\gamma(\tau) = \begin{cases} 1 & \text{if } |\tau| ≤ K \\ 0 & \text{if }|\tau| > K \end{cases}$$ where $K$ is a positive integer. Is $\gamma(\tau)$ an auto ...
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### Is it correct to estimate covariance matrix of null distribution of related random variables using independent groups as data points?

I will use an example of an antidepressant drug trial as an example to illustrate my question - hope this helps as I, too, am confused. Suppose a study is testing the effects of some drug on people ...
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### What's exactly inside the attribute 'Pars' in apVar of the lme object in R

In this example: what is the third term in attr(,"Pars") within the apVar of the ...
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### Using covariance matrix as data for linear discriminant analysis?

In PCA analysis, covariance matrix as input is often used. But for LDA, it seems that it's not so usual. Is there any reason why covariance as data is not used well as a standard for LDA?
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I'm trying to calculate a 2x2 covariance matrix in Cartesian coordinates that represents the amount of uncertainty when rotating and translating a point in 2D space, $\Sigma = \begin{pmatrix} \sigma_{... 0 votes 0 answers 17 views ### Square-root matrix of coefficient var-cov matrix$\mathbf{V}(\boldsymbol{\beta})$during simulation I am performing simulations to obtain predicted yhat values based on fixed x-values and random coefficient values about their uncertainty. The matrix with random values of coefficients$(m \times p)$... 1 vote 0 answers 17 views ### How to build the covariance matrix with different weighted moments via GMM [closed] I have two sets of moment conditions, one is IV moment with N observations but the second moment only has N_1 observations, N_1<N. How to build the covariance matrix? Appreciate for any replies! 1 vote 1 answer 120 views ### Difference of the conditional variance-covariance matrices between lme4 and nlme In ?lme4::ranef, it is stated: condVar: a logical argument indicating if the conditional variance-covariance matrices of the random effects should be added as an ... 4 votes 3 answers 175 views ### Looking at how covariance/correlation between variables differs in two groups? I have a few hundred variables representing different biomarkers. These variables have been measured in both cases and controls. The underlying units of measurement are not important, so I have ... 1 vote 0 answers 7 views ### Analyse clustered items from different scales? I am a non stat person so pls be kind in your reply! What sort of statistic can I use to compare how the items of 3 different Likert scales covariate? My respondents sample is 150 ppl. Each respondent ... 1 vote 1 answer 60 views ### When to use 'unconditional = FALSE' in plot.gam() I'm trying to figure out under what conditions one would make 'unconditional = FALSE' (in plot.gam and gratia::draw), because in my case 'unconditional = TRUE' shrunk the uncertainty bands around my ... 0 votes 0 answers 66 views ### Evaluate relative quality of covariance matrix relative to a set My ultimate goal is a way to evaluate a group of "m" covariance matrices (all size n*n) so I can pick an arbitrary one and calculate "this one is tighter than the average covariance ... 0 votes 0 answers 36 views ### Gaussian copula: how to scale data back to get target covariance matrix (not correlation) I would like to use a Gaussian Copula to simulate data with a given covariance matrix and given marginal distributions. I understand that the input to the copula cannot be the covariance matrix$\...
Given a symmetric positive definite matrix $\bf \Sigma \in \mathbb{R}^{n \times n}$, I want to find a matrix ${\bf \Gamma} \in \mathbb{R}^{n \times n}$ and a vector ${\bf m} \in \mathbb{R}^n$ such ...
Problem In several applications in surveys, it would be helpful to be able to generate a set of $R$ $n$-dimensional variates with the following properties: Has mean vector $1$ Has a specified ...