Covariance is a quantity used to measure the strength and direction of the linear relationship between two variables. The covariance is unscaled, & thus often difficult to interpret; when scaled by the variables' SDs, it becomes Pearson's correlation coefficient.

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How to calculate the estimation error of portfolio variance using propagation results?

I am trying to find a conservative approximation for the propagated estimation error of a investment portfolio's variance (comprising two assets), given we know the estimation error for the variance ...
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1answer
15 views

Perfect correlation and covariance matrices

When a covariance matrix is a diagonal matrix then there is no correlation between random variables as seen here Difference between identity and diagonal covariance matrices However, what if I wanted ...
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3 views

Minimum Covariance Determinant (MCD) vs DCC GARCH

I've been reading about various covariance estimation techniques in an attempt to understand which one has performed the best. In this paper, the authors conclude that DCC GARCH outperforms most ...
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24 views

Help understanding a kriging variation for bare earth extraction

Problem: The authors of a paper (http://www.isprs.org/proceedings/XXXIV/part3/papers/paper106.pdf) develop a bare earth extraction algorithm for LiDAR that is based on kriging. What I don't ...
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6 views

Correlation between two variables from muli-dimensional distribution?

Possibly an elementary question, however I can't find an satisfactory answer. If I have a bivariate distribution, then clearly its easy to determine the correlation between those two variables, For ...
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1answer
31 views

Minimum covariance of 2 random variables given the covariance of each with a third random variable

If we have 3 random variables, with the first two with a covariance of 0.1 and the second two with a covariance of 0.1, what is the minimum covariance of the first and third? Is there a generalized ...
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9 views

Sum of covariances equals variance of sum OR: how to estimate the relative importance of a time series for a sum of time series?

I have n time series x1, ..., xn and the sum of these time series xsum = x1 + ... + xn. I observed that the sum of all covariances between each time series and their sum equals the variance of that ...
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14 views

Regression coefficients in terms of means, st.devs and correlations [duplicate]

I am dealing with bivariate regression. Can somebody post formulas for the betas in terms of means, covariances, correlations, etc. i.e. summary statistics rather than the actual, full data set?
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47 views

How to invert a sparse covariance matrix for spatial data on a grid?

Say we have some gaussian random variables that can be indexed on a grid. A convolution was applied to this grid, so now there is covariance between the grid points. The covariance is given by (see ...
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13 views

Covariance matrix from independent measurement errors

I need to implement covariance matrices for a maximum likelihood calculation. Let me skip all details and come to the part that bothers me. I have a series of measurements and for each measurement I ...
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1answer
73 views

Generate t distributed random variable in matlab

How can we generate t distributed random variables with given mean and covariance in matlab. trnd is a function in matlab but we can get random variable with different degrees of freedom but how to ...
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21 views

Is covariance a measure of effect size?

Is covariance a measure of effect size? Since correlation is such a measure, and correlation is normalized covariance, I would think so, but I'd like to know for sure.
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1answer
23 views

What is the covariance when you know the covariance w.r.t. a common variable?

Say you know that ${\rm var}\Bigg( \begin{bmatrix} {\bf x}_1 \\ {\bf x}_2 \end{bmatrix}\Bigg) = {\bf \Sigma} = \begin{bmatrix} {\bf \Sigma}_{11} & {\bf \Sigma}_{12}\\ {\bf \Sigma}_{21} & ...
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1answer
48 views

Relationship between Gram and covariance matrices

For a $n\times p$ matrix $X$, where $p \gg n$, what is the relationship between $X^{T}X$ (scatter matrix, on which covariance matrix is based) and $XX^{T}$ (outer product sometimes called Gram ...
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0answers
20 views

Which statistical method can I use to see if there is a correlation between data sets with different size?

For my thesis I want to compare the 3 different test results. If the results are more than 5, samples are failed. And I want to show if these tests are similar behaviour (if there is a correlation ...
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36 views

How to determine stationarity, mean and covariance?

I'm having some trouble with some questions for an assignment that I need to do. The question asks to determine whether or not a process is stationary and if it is, what is its mean and covariance. ...
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1answer
27 views

How does the variance-covariance matrix change when I create a linear combination of two variables? [duplicate]

Suppose I have four normal r.v (X,Y,W,Z) and the variance-covariance matrix is know. If I create a new r.v J=aX+bY (a and b are scalar), what is the new variance-covariance matrix? Thank you
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25 views

Is log partition function guaranteed to be convex

In a paper by Wainwright and Jordan on page 62 it mentions that a log partition function is always convex. This is done by showing that the second derivative of the log partition function is the ...
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2answers
107 views

How is it possible to have a significant correlation between two variables but a low covariance?

How is it possible to have a significant correlation between two variables but a low covariance? What does this mean?
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30 views

Calculate Var(X/Y) for dependent variables?

I understand that you can calculate Var(X*Y) through Bienayme, whether variables are dependent or not. I am wondering if there is a similar way of calculating Var(X/Y) when variables are dependent? ...
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0answers
10 views

Covariance matrix of estimated parameters of SVAR

How to get covariance matrix of estimated parameters of structural VAR? Any reference, if possible. Thank you in advance.
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0answers
12 views

How does unbiased cov.wt compute its value?

What is exactly the calculation used when calling cov.wt((faithful,c(1,2,3,4))$cov)? (Say the data faithful has 4 rows and 2 columns, coordinates x,y) I.e.: What ...
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1answer
58 views

A sufficient statistic for Laplace distribution

Suppose we have p dimensional vector of $X =[X_1 \dots X_n]$ where X is Laplace distributed. What will be a sufficient statistics for estimating covariance of $X$? Would it be the sample ...
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1answer
24 views

Covariance between a variable and an interaction variable

If I have two independent variables $X$ and $Y$, then $Cov(X,Y)=0$. Now let $Z = X*Y$. Then I would assume $Cov(X,Z)\ne 0$, but given the expecations, variances and covariances of $X$ and $Y$ is there ...
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0answers
14 views

Variance of sum of datasets with different sampling intervals

I have two randomly distributed datasets which are to be added together element-wise, and I am looking to calculate the uncertainty of the mean of the result. One dataset had a sampling rate of 1 ...
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23 views

How to equal weight and value weight a portfolio of mutual fund returns?

I have the historical monthly returns of around 3000 mutual funds. How would I equal weight them? And does 'value weighting' them include multiplying each set of fund returns by a factor ...
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1answer
14 views

Gaussian Mixture Model: bandwidth parameter versus variogram fitting?

I'm estimating a stationary, spatially random variable over a 2-dimensional domain. I have ground-truth measurements in several locations, over time. I need some way of spatially-interpolating ...
2
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1answer
158 views

Scaling a Covariance Matrix by a factor?

I have a $n\times n$ covariance matrix representing the covariance between n random processes. I want to increase all of the covariances by a certain factor, say $1.5x$. Multiplying each covariance ...
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22 views

In logistic regression, what is the expected correlation between prediction and the dependent variable?

In multiple logistic regression: what is the expected covariance between the dependant variable $Y_i$ and prediction $expit(X_i\hat{\beta})$? what is the expected covariance between the dependant ...
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1answer
47 views

Maximum likelihood estimation for Cauchy noise

What is the maximum likelihood estimator of the covariance matrix for a given vector in the presence of Cauchy noise? How can we calculate it given that the Cauchy distribution has infinite variance? ...
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38 views

high correlated variables -> ill-conditioned covariance matrix?

I was wondering why the covariance matrix of high correlated variables is ill-conditioned. Is there any (logical) explanation for this? Thanks!
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19 views

Covariance Matrix vs. Pairwise Covariance Matrix?

I found this equation here to calculate a covariance matrix of any number of variables using matrix algebra. $1/N(X - 1\bar{x})^T(X - 1\bar{x}^T)$ For a given matrix $X$ with $N$ samples. The ...
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2answers
127 views

What is the expected value of $\frac{X}{X+Y}$?

I am trying to find the expected value of $\displaystyle E\Bigg[\frac{X}{X+Y}\Bigg]$. I started with writing $\displaystyle E\Bigg[\frac{X}{X+Y}\Bigg] = ...
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9 views

Picking the Right Co-Variance

I am conducting a repeated measures regression, in a linear mixed model. I am also analyzing the data with a general estimating equation. The dependent variable is continuous (a measure of arousal) ...
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1answer
39 views

Alternative parameterization for the covariance matrix via Euler angles

Using spectral decomposition, we can write any symmetric matrix as $$\Sigma = Q \Lambda Q^{\top}$$ where $Q$ is orthonormal, and $$\Lambda = \text{diag}(\lambda_1, ..., \lambda_p)$$ with ...
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18 views

General definition for higher order co-moment matrix

Is there a general equation or procedure for computing higher-order co-moment matrices (i.e., coskewness matrix, cokurtosis matrix, etc) for a vector of random variables? For example, the covariance ...
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0answers
10 views

Correct formula for unbiased estimate of population covariance [duplicate]

Is this formula a correct way to estimate population covariance from a sample? $$s_{xy} = \frac{1}{n-1}\sum\limits_{i=1}^{n}(x_i-\bar{x})(y_i-\bar{y})$$
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72 views

How can I extract a residual variance-covariance matrix in lme?

I have been using MCMCglmm in R to fit bivariate (two response traits) mixed models in R, but now I need to move to lme to account for temporal autocorrelation of the residuals. In MCMCglmm I can fit ...
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0answers
20 views

Covariance of ARMA (2,1)

I am preparing for an exam and need help. Consider the following estimated ARMA(2,1) model, $$y_t = 0.05 + 0.83y_{t-1} + 0.13y_{t-2} - 0.15e_{t-1} + e_t$$ Given the unconditional variance and 1st ...
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1answer
23 views

How do you define the structure of a Covariance Matrix

I am reading a paper by Ledoit and Wolf,2001 on Improved Estimation of the Covariance Matrix of Stock Returns. I am a little confused by some points, and will appreciate a broader explanation. The ...
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37 views

Fit multiple regression model with pairwise deletion (or on a correlation/covariance matrix) in R

I'm trying to fit a multiple regression model with pairwise deletion in the context of missing data. lm() uses listwise deletion, which I'd prefer not to use in my ...
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34 views

slope comparisons given by independant measurements

With the data used in a previous question matplot/ggplot2 ...
4
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2answers
88 views

Is $\text{Cov}(|a|,|b|)\geq \text{Cov}(a,b)$?

The above seems intuitively true, (where $|a|$ refers to the absolute value of $a$), but I'm struggling to prove it - would be very grateful for either a proof or a reference.
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19 views

Computing covariance between normal and uniform distributions

I think that this question is related: Covariance of a compound distribution, but it's too abstract for me (I believe that what I have to do must be simpler). Here's the given: machines $A$ and $B$ ...
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24 views

Testing for structural break in the covariance

I estimated a bivariate VAR(p) model and assume that there exist two covariance regime $\Sigma_1$ for the period 1 to $T_B$ and $\Sigma_2$ for the period $T_B+1$ to $T$. I am now interest in testing ...
3
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0answers
61 views

Does a “pruned” i.i.d. multivariate sample behave as the i.i.d. sample?

Let $z_1,\cdots,z_n$ be $n$ points drawn i.i.d. from $\mathbb{C}N_p(0,\Sigma_n)$. The distribution of the covariance $S_n=\frac1n\sum_{i=1}^n z_i z_i^*$ is well known in the limit as $n,p(n)\to\infty$ ...
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1answer
32 views

How do i show multiplication of covariances?

i am trying to show the following $$Cov(a,b) = \frac {Cov(a,x) * Cov(b,x)} {Var(x)}$$ I am a bit lost on how to expand the numerator term, so i wrote the following $$Cov(a,b) = \frac ...
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Multifactor Covariance Matrix

hanks for taking a look. I am struggling to understand a rather simple concept. I ran a simple linear regression of the form $$A= \alpha+ \beta X + E$$ $$C = \alpha +\beta X + E$$ Then i ...
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On the correlation function of a stationary time series (spectral analysis)

I am following a proof of the following fact of which I do not understand only the last step. I will post it entirely for the sake of completeness but do not hesitate to just look at my question at ...
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Distribution of the maximum vector (over i.i.d. set) and its dot product with the eigenvectors spanning the rest.

Let $z_1,\dots,z_n$ be i.i.d. draws from $N(0,\Sigma)$, where $\Sigma$ is a $p\times p$ matrix. Assume that $p>n$. Suppose (up to re-labeling) that $z_n=\max_i \|z_i\|_2$. Consider the eigenvectors ...