The variance-covariance matrix, or sometimes just covariance matrix, is the matrix whose $(i,j)$ element is the covariance between the $i^\text{th}$ and $j^\text{th}$ variable (or the $i^\text{th}$ and $j^\text{th}$ parameter).

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Is every correlation matrix positive semi-definite?

I am generating correlation matrix by some new algorithm. Generated matrix is non positive semi definite matrix. I'm getting few negative eigenvalues. Rest of eigenvalues are quite equal to ideal ...
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Matlab: How to implement inverse of determinant of covariance-variance matrix [on hold]

I have asked this Question http://stackoverflow.com/questions/27068927/matlab-variancecovariance-matrix and repeating it here because I am unsure where it will probably get an answer. When solving ...
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Multivariate normal with singular covariance

I'm an undergraduate student. I read about multivariate normal distribution in hogg and craig. And i wonder why the covariance is allowed to be positive SEMI-definite. I read this Normal distribution ...
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How to generate a large full-rank random correlation matrix with some strong correlations present?

I would like to generate a random correlation matrix $\mathbf C$ of $n \times n$ size such that there are some moderately strong correlations present: square real symmetric matrix of $n \times n$ ...
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Can the law of total covariance apply to variables from different sample spaces?

Wikipedia says this about the law of total covariance (http://en.wikipedia.org/wiki/Law_of_total_covariance): In probability theory, the law of total covariance,[1] covariance decomposition ...
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Confused about the visual explanation of eigenvectors: how can visually different datasets have the same eigenvectors?

A lot of statistics textbooks provide an intuitive illustration of what the eigenvectors of a covariance matrix are: The vectors u and z form the eigenvectors (well, eigenaxes). This makes sense. ...
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40 views

How to select a subsample of fixed size to maximize its total PCA variance?

I would like to use PCA to help design my genomics experiment. I can only afford to perform my experiment on a limited number of genotypes so would like to maximize the variation of the ones I ...
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20 views

Can any one give me inf how I can form X, Z, R, G, and A matrices using dummy variables using the posted info below?

Y=Xb +Zu + e, where y represents a vector of observed (measured) phenotype values, b is vector of unknown parameters for “fixed" effects, while X is corresponding design matrix, u is vector of ...
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57 views

What is the correct formula for between-class scatter matrix in LDA?

At one point in the process of applying linear discriminant analysis (LDA), one has to find the vector $v$ that maximizes the ratio $vBv'/vWv'$, where $B$ is the "between-class scatter" matrix, and ...
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17 views

covariance matrix of residuals from a fitted model to decorrelate residuals

I fit a geeglm model with clustered data and now I would like to decorrelate the residuals of the model in order to run model diagnostics. I read that if I can obtain the covariance matrix of the ...
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1answer
68 views

Variance of Beta IV

I'm trying to calculate the variance of the Instrumental Variables (IV) estimator $${\hat \beta _{IV}} = {\left( {{Z^T}X} \right)^{ - 1}}{Z^T}y = \beta + {\left( {{Z^T}X} \right)^{ - 1}}{Z^T}u$$ (or, ...
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37 views

Correlated random draws with graph structured correlation

I have a problem where I have a graph structure, such that some nodes are connected to other nodes i.e. we have an adjacency matrix of size n*n with a 1 corresponding to a connection and 0 otherwise. ...
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58 views

What are the implications of estimating a covariance matrix from a correlated sample?

Given a sample of $n$ independent observations $x_1,...,x_n$ (where $x_i$ are $p$-dimensional column vectors), the $p \times p$ sample covariance matrix is defined as ...
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1answer
56 views

Determinant of the covariance matrix in a normal distribution

Suppose a $p \times 1$ vector $x \sim N_p(\boldsymbol 0, \boldsymbol \Sigma_1)$. Now, There is another covariance matrix $\boldsymbol \Sigma_2$. We know that $|\boldsymbol \Sigma_2| < |\boldsymbol ...
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What if the variance-covariance matrix of a sum of two random vectors? [duplicate]

If X is a px1 random vector with mean Mu(x) and variance-covariance matrix sigma(x) and if Y is a qx1 random vector with mean Mu(y) and variance-covariance matrix sigma(y). If p=q, what would be the ...
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1answer
20 views

Comparing and Interpreting covariances

I had a discussion about covariance recently and it would be nice to hear your feedback about this. Let's say we have a dataset of $n$ samples with $d$ attributes. For simplicity, let's say 3 of ...
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1answer
57 views

Manual calculation of variance-covariance from published confidence intervals

I would like to obtain the variance-covariance matrix from a published set of regression outputs. These outputs provide a mean value and confidence intervals. I will convert the confidence intervals ...
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12 views

Estimating covariance for naive Bayes

I am a beginner in Pattern Recognition and started reading up Bayesian classifiers. I came across the case of naive Bayes with equal covariance in all dimensions. Given sufficient data, how does one ...
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119 views

How to interpret glmer results (variance, correlation and ICC)

I'm a beginner in statistics and I have to run multilevel logistic regressions. I am confused with the results as they differ from logistic regression with just one level. I don't know how to ...
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1answer
68 views

Correlation between two normally distributed variables

Let a~$\mathcal{N}(\mu_a,{\sigma_a}^2)$,b~$\mathcal{N}(\mu_b,{\sigma_b}^2)$ and c~$\mathcal{N}(\mu_c,{\sigma_c}^2)$. We construct two normal variables x~$a-b$ and y~$a-c$. Can we find the ...
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21 views

Can you combined two sources with difference variance to reduce error? [duplicate]

I have two samples of data each estimates of a position x, y with Gaussian noise. One source has a larger variance than the other. Is this source in any way useful ...
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98 views

Inverse covariance matrix, off-diagonal entries

Let $\Sigma$ be a covariance matrix. According to the material in this link, If the elements of $\Sigma$ are all positive, most of the off-diagonal elements in $\Sigma^{-1}$ will be negative ...
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34 views

Variance-covariance matrix as the sum of variance covariance matrices

I have a variance-covariance matrix, $\mathrm{V}$. This allows me to take a vector, $x$ of independent random variables drawn from a known distribution, and induce a required variance-covariance ...
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54 views

Negative variance from inverse Hessian matrix

I used nlm function in R to do the optimization. When I calculated the correlation between estimated parameters using the inverse of Hessian matrix, I got negative values on the diagonal. My questions ...
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50 views

Covariance matrix estimation in presence of missing data

I want to estimate a covariance matrix from data with some missing values. Ideally I'd like an R package but python could be ok. R has some built in ways of doing this. You can use ...
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62 views

What is the best way to simulate data for a linear regression model?

I am concerned with simulating data for a linear regression model. I need to control the means, variances, and correlations (covariances) between the predictors and the criterion variable. In ...
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1answer
64 views

Expectation of the product of two log normal variables

I am struggling with a proof, and I am wondering if anyone can help or point me to the right direction. Suppose that we have two variables, $X$ and $Y$, and they follow a multivariate normal ...
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1answer
44 views

Comparing two variance matrices

I am looking for bibliographical reference for comparing two variance matrices with he following criterion: $\text{Var}[X] \geq \text{Var}[Y] \quad \text{if} \quad \text{Var}[X]-\text{Var}[Y] \succeq ...
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101 views

How to use the Huber/White estimator of covariances in a generalized linear mixed model (glmmPQL) in R?

An analysis was implemented in SPSS 22 that uses the "Generalized Linear Mixed Models" feature of the program. Now I am looking for a way to port this to R. I use the glmmPQL() function of the MASS ...
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136 views

Is there a way to use the covariance matrix to find coefficients for multiple regression?

For simple linear regression, the regression coefficient is calculable directly from the variance-covariance matrix $C$, by $$ C_{d, e}\over C_{e,e} $$ where $d$ is the dependent variable's index, ...
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1answer
99 views

Variance-covariance matrix for ridge regression with stochastic $\lambda$

In ridge regression with design matrix $X$, outcomes $y$, fixed regularization parameter $\lambda$, and errors $\epsilon\sim\mathcal{N}(0, \sigma^2I)$, the computations for the ridge regression ...
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72 views

Whitening Transformation using a Hadamard product Variance Matrix

I want to whiten a vector $X$ by transforming the variance-covariance matrix so the variance-covariance matrix of the transformed series will be the identity matrix $I$. $X$ is a time-series column ...
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40 views

Cholesky decomposition and confidence ellipsoid

I'm trying to construct an error ellipsoid from a covariance matrix (which exists for a 3D point) and then sample consistent xyz points in this region. (This question succeeds this one.) What I'm ...
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34 views

Testing the random slope with correlated random effects

I have a mixed/random effects model $$\mathbf{y}_i=\mathbf{X}_i\boldsymbol\beta+\mathbf{Z}_i\mathbf b_i+\boldsymbol\epsilon_i,$$ where random effects $\mathbf b_i$ has variance-covariance matrix ...
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104 views

Trying to use Cholesky decomposition of covariance matrix to sample error ellipsoid

I'm trying to construct an error ellipsoid from a covariance matrix (which exists for a 3D point) and then sample consistent xyz points in this region. In a previous question when I asked about this ...
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1answer
34 views

Univariate Normal Converted to Multivariate Normal: Covariance Derivation

I am reading the paper available at this link: https://drive.google.com/file/d/0B2_rKFnvrjMARnU1QjB4anR3RDA/edit?usp=sharing I am having trouble understanding section 5.1 (page 2741). Essentially ...
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60 views

Weighted sample covariance

I have read the Wikipedia article, and know that the unbiased weighted sample covariance matrix for the row vector $\mathbf{x}_i$ is $$\Sigma=\frac{1}{\sum_{i=1}^{N}w_i - 1}\sum_{i=1}^N w_i ...
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Implications of doing a confirmatory factor analysis with a correlation matrix as input instead of a variance-covariance matrix?

Is this possible, and if so what are the implications of doing things one way rather than another. Is one approach generally preferable? So far I have only been taught to use a variance-covariance ...
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2answers
162 views

How to calculate variance - covariance matrix of a matrix?

For example, we have an NxP matrix with N rows and P variables. Then we need to calculate a PxP sample covariance matrix. How do I do that?
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Is it necessary to transform an econometric model in order to have only diagonal elements in the error covariance matrix?

Model and its assumptions I'm working on the methodology of a two-way error component model. Here is the model: $$y_{jis} = x_{jis} \beta + \upsilon_{jis}$$ $j$ refers to school, $i$ refers to ...
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169 views

Background subtraction for signal and error analysis

I use a CCD to see the split of a energy level due to Zeeman effect. I have a 1 dimensional CCD of 7926 pixel of 7μm each one. My CCD analyze a region 2 dimensional, and then it steps forward 200 ...
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44 views

Parameter covariance matrix for a multivariate (matrix-Y) logit model

I've got a partially-observed unidirectional network. Nodes can be linked (0/1) in one of many ways. For now, lets call them $y_1$ and $y_2$. The unit of analysis is the potential network link ...
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1answer
389 views

Gelman and Rubin convergence diagnostic, how to generalise to work with vectors?

The Gelman and Rubin diagnostic is used to check the convergence of multiple mcmc chains run in parallel. It compares the within-chain variance to the between-chain variance, the exposition is below: ...
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1answer
36 views

Mean of covariance matrices

I'm trying to generalise a formula that takes the mean of some variances to it work with vectors. I'm not sure it makes sense to take the variance between a bunch of vectors, rather it is more suited ...
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71 views

Problems estimating covariance matrices with small $n$, smaller $p$?

It is well known that estimating large covariance matrices from small samples is problematic. For instance, the $p \times p$ sample covariance matrix $\Sigma_n$, estimated from $n$ samples, is not ...
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Sample covariance matrix

$\newcommand{\X}{\mathbf{X}} \renewcommand{\S}{\mathbf{S}} \newcommand{\I}{\mathbf{I}} \newcommand{\1}{\mathbf{1}} $ I found an article with an unusual (for me) covariance matrix. Let $\X$ denote an ...
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How to determine the confidence interval or significance of a covariance estimate

I was wondering if there is a way to determine the significance of a covariance? So, if have two vectors of returns, and then calculate the covariance, how do I determine if the sample covariance is ...
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59 views

Specific variance covariance structure in lmer

I have a dataset with cluster correlated data; multiple measurement on the same subject (not over time). I am trying to create two different mixed models using lmer in R with two specific variance ...
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1k views

Variance-Covariance matrix interpretation

Assume we have a linear model Model1 and vcov(Model1) gives the following matrix: ...
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178 views

Significant box's test equality covariance matrices, How bad it is?

Having equal number of cases across two groups (60 total cases), if one wants to perform a split-plot Anova and finds out that the Box's Test of Equality of Covariance Metrices is less than 0.001 then ...