Is a measurement of the strength and direction of the linear relationship between two variables. The covariance between $X$ and $Y$ is defined as $${\rm cov}(X,Y) = E \left[ \left( X-E(X) \right) \left( Y-E(Y) \right) \right] = E(XY) - E(X)E(Y) $$ Since the magnitude is difficult to interpret in ...
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5 views
Confusion related to dual problem formulation in sparse inverse covariance matrix estimation
I was reading this paper where they are trying to estimate the inverse covariance matrix of the gaussian. What they are trying to maximize the gaussian log likelihood. The primal problem is maximize ...
0
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0answers
19 views
Sorting/Clustering similarity matrices
I wonder, what are the available libraries in R or Python to do correlation matrix clustering (sometimes it is referred to clustering).
I also, wonder, after clustering/grouping each point. What is ...
2
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2answers
51 views
Estimating the covariance of the means from two samples?
Let there be two samples of size $n$, $x_i$ and $y_i$ from two different normal distributions.
What is $\operatorname{cov}(\bar X_n, \bar Y_n)$? And how can it be estimated?
The motivation for my ...
0
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1answer
31 views
Confusion related to minimization of a gaussian likelihood function
I have this confusion related to minimization of gaussian likelihood function. The negative of the log likelihood of gaussian distribution is
$-\log \det(Q) + \text{tr}(SQ) + \lambda||Q||_{1}$ where ...
0
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0answers
19 views
Combining covariances
Imagine we have one sample (n=40) from a population on 2 variables, for which we estimate the covariance (say, 0.1). If we would have another sample (n=10) from the same population, and we estimate ...
1
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0answers
39 views
Interpretation of Variance and Covariance
I am totally new to statistics and I have to create a variance and covariance analysis.
I am using SPSS for this.
I have created the covariance table:
Hopefully it is the right thing. The first 3 ...
2
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1answer
34 views
Proof of a PD covariance matrix for conditional Gaussian
I was looking at the formula for the conditional covariance of a partitioned matrix. I understand the intuition behind the equation for the conditional covariance, but I'm not sure how to show that ...
0
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0answers
24 views
calculating variance of sum of predicted costs from two-part model
I have a question regarding the calculation of the variance of the sum of predicted health care costs using a two-part regression model. Details are below, but it boils down to how to calculate the ...
0
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0answers
16 views
Covariance of function uncertainty, why (J^T)*S*J? [duplicate]
As I understand it; to get the uncertainty of a function that is based on some measurements, the derivative of this function with respect to this measurment has to be calculated, and multiplied by ...
1
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1answer
43 views
Covariance of a set of uniformly distributed unit vectors?
I have a set of uniformly distributed unit vectors within a "cone" (essentially a subset of a uniform distribution on the unit sphere, as described here). I've found how to get the covariance matrix ...
0
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1answer
51 views
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 = ...
10
votes
2answers
358 views
Is every covariance matrix positive definite?
I guess the answer shoule be yes...but I still feel something not right. But there should be some general results on literature, could anyone help me. Thanks a lot.
0
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2answers
74 views
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 ...
2
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2answers
97 views
How can I find $\text{Cov}(X_k,X_5)$
There are $10$ empty boxes numbered $1, 2, \dots , 10$ placed sequentially on the circumference of a circle.We perform $100$ independent trials. At each trial, one box is selected with probability ...
0
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0answers
85 views
ANCOVA (GLM) versus Mixed Linear Model with covariate measured at both pre- and post-treatment (in SPSS)
I'm trying to analyze a pre/post study with 4 treatment groups. The Dependent Variable, Speed, measures how quickly a person's facial expression reaches peak intensity; this measure is normally ...
0
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0answers
38 views
Assuming in a regression model that all off-diagonal elements of the beta-hat variance-covariance matrix are zero?
What are the implications of assuming in a regression model that all off-diagonal elements of the beta-hat variance-covariance matrix are zero?
Assuming all zero off-diagonals in the ...
6
votes
1answer
155 views
Covariance matrix for Gaussian Process and Wishart distribution
I'm reading through this paper on Generalised Wishart Processes (GWP). The paper calculates the covariances between different random variables (following Gaussian Process) using squared exponential ...
0
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2answers
168 views
Given a table defining the joint probabilities, how do I calculate certain parameters of the marginal distributions?
The number of items sold on any one day in the traditional shop is a random variable X and the corresponding number of items sold via the Internet is a random variable Y. The joint distribution of X ...
3
votes
2answers
267 views
Is a sample covariance matrix always symmetric and positive definite?
When computing the covariance matrix of a sample, is one then guaranteed to get a symmetric and positive-definite matrix?
Currently my problem has a sample of 4600 observation vectors and 24 ...
3
votes
1answer
136 views
Test to show when diverging linear regression models are statistically different
What method will allow me to identify the values of the independent variable where two (or more) diverging linear regression models are statistically different?
e.g.
Take two simple linear ...
0
votes
1answer
120 views
Show that $E(XY) = σ_{XY} + μ_Xμ_Y$?
Let X and Y be two random variables with means $μ_X$ and $μ_Y$ , variances $σ^2_Y$, $σ^2_X$ and covariance $σ_{XY}$ . Show that $E(XY) = σ_{XY} + μ_Xμ_Y$?
I tried the Covariance formula with:
...
4
votes
1answer
107 views
Combining two covariance matrices
I'm calculating the covariance of a distribution in parallel and I need to combine the distributed results into on singular Gaussian. How do I combine the two?
Linearly interpolating between the two ...
1
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1answer
52 views
quantifying interaction between variables in an equation
What do I need to measure interaction between variables in a particular equation?
For e.g.
Me just taking 50 grams of protein everyday will help me health wise.
Me just doing exercise for 1 hour ...
0
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0answers
65 views
How covariance matrix is computed in generalized linear model?
In R I can compute a covariance matrix of glm by vcov function. I wonder how this computation works?
1
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0answers
89 views
Weighted covariance matrix using kernels
I would like to create a weighted covariance matrix (say 5 variables) using 3 different time points where the weights come from a kernel function (can be normal, triangular, etc) but I'm not ...
2
votes
2answers
399 views
Numerical Instability of calculating inverse covariance matrix
I have a 65 samples of 21-dimensional data (pasted here) and I am constructing the covariance matrix from it. When computed in C++ I get the covariance matrix pasted here. And when computed in matlab ...
0
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0answers
96 views
Singular value decompostion covariance matrix (numerical recipes)
I am trying to implement singular value decomposition in C. I am using routines svdfit and svdvar from Numerical Recipes.
The results from svdfit seem to be correct, but the results from svdvar are ...
4
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1answer
155 views
Can I convert a covariance matrix into uncertainties for variables?
I have a GPS unit that outputs a noise measurement via covariance matrix $\Sigma$:
$\Sigma = \left[\begin{matrix}
\sigma_{xx} & \sigma_{xy} & \sigma_{xz} \\ \sigma_{yx} & \sigma_{yy} ...
0
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0answers
92 views
Covariance of binary and continuous variable
Suppose $y$ is a continuous random variable and $d$ is a binary random variable that takes the value $1$ with probability $p$ and $0$ with probability $1-p$.
How do I show that ...
0
votes
1answer
60 views
Factor intercorrelations and model design
Having done an exploratory factor analysis (SPSS), what exactly can I infer from the factor intercorrelation table that is output after the factors are extracted/rotated?
If two factors are ...
0
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0answers
85 views
How does Newey-West covariance help increase accuracy of OLS estimates?
I have implemented a model using OLS estimates, but the results don't look too good. I've come across this term 'Newey-West covariance', and that I need to use residuals from my model as input, but ...
0
votes
1answer
131 views
Covariance of a bivariate Gaussian given identity matrix
I have a homework problem about finding an optimal decision boundary. I know the formula (not really the process) for calculating one, so that may be another question entirely, but I do know I need ...
0
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0answers
148 views
proving sample covariance is unbiased with matrix algebra [closed]
Given an i.i.d. sample $(x_i,y_i)$ of size $n$ from a bivariate distribution $(x,y)$, I'm trying to prove that the sample covariance $$\frac{1}{n-1}\sum_{i=1}^n(x_i-\bar{x})(y_i-\bar{y})$$ is an ...
0
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0answers
54 views
Estimation of max likelihood sample mean and sample covariance
How do I estimate the maximum likelihood sample mean and sample covariance of the data set consisting of
N = 100 2-dimensional samples x = (x1 , x2 )T ∈ R2 drawn from a 2-dimensional Gaussian ...
0
votes
0answers
28 views
Ensuring the covariace matrix is invertible [duplicate]
I know that when constructing a sample covariance matrix from d-dimension vectors we need at least $d+1$ samples. But are there any other constraints to ensure that the matrix will be invertible?
3
votes
2answers
264 views
Ways to measure distance from multivariate Gaussian (Mahalanobis distance)
I have a cluster of p-dimensional points and given a new p-dimensional point $x$ I want to determine whether or not it is likely to belong to this cluster.
The cluster is made up of $n$ ...
4
votes
1answer
175 views
Intuitive understanding covariance, cross-covariance, auto-/cross-correliation and power spectrum density
I'm currently studying for my finals in basic statistics for my ECE bachelor.
While I think I have the math mostly down, I lack intuitive understanding what the numbers actually mean.(Preamble: I'll ...
2
votes
1answer
292 views
What to do when sample covariance matrix is not invertible?
I am working on some clustering techniques, where for a given cluster of d-dimension vectors I assume a multivariate normal distribution and calculate the sample d-dimensional mean vector and the ...
0
votes
0answers
217 views
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 ...
3
votes
1answer
89 views
covariance of RVs under a nonlinear transformation
I have a multivariately distributed random 3-vector
...
0
votes
0answers
26 views
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 ...
2
votes
1answer
65 views
How to interpret the sum of the elements of an inverse covariance matrix?
In the derivation of global minimum variance portfolio, we get The $(Σ^{-1}1) /(1'Σ^{-1}1)$. What's the meaning of $1'Σ^{-1}1$ and $Σ^{-1}1$. $Σ$ is a covariance matrix of assets returns.
0
votes
0answers
75 views
How to derive the partial correlations interpretation of inverse covariance matrix?
How to derive the partial correlations interpretation of inverse covariance matrix by using the Schur complement to get a formula for the entries of the inverse covariance matrix in terms of the ...
5
votes
1answer
79 views
Distribution of eigenvalues given one is known
I'm familiar with using insights from Random Matrix Theory to determine the number of principal components from the PCA of a covariance/correlation matrix to use to form factors.
If the eigenvalue ...
3
votes
0answers
109 views
Standard error of estimates of covariance parameterized in tems of cholesky
In unconstrained optimization, covariance matrix $C$ is parameterized in terms of its Cholesky ($C=LL^\prime)$. In other words, the parameter vector $\theta$ involves elements of the lower triangular ...
2
votes
0answers
55 views
Finding correlation coefficient
if I have A and B with the following known variables:
with $E[A]$, $E[B]$ , $\sigma_{A}$ , $\sigma_B$
and correlation coefficient: $\rho_{AB}$ (assign numbers if you like)
Say: $C=0.6A+0.4B$
Then ...
0
votes
1answer
174 views
Solving PCA with correlation matrix of a dataset and its singular value decomposition
Suppose I have a $d \times n$ matrix $\mathbf X$ (each entry point has $d$ dimensions) and after some manipulation of data (i.e. summarizing the data $\mathbf X$) I get its $d \times d$ symmetric, ...
2
votes
1answer
94 views
Pearson correlation of one log-transformed variable
Consider two $X$ and $Y$ that are bivariate lognormal. Is there a way to express $\newcommand{\Cov}{\mathrm{Cov}}\Cov(\log(X),Y)$ in terms of $\Cov(X,Y)$, even if an approximation must be made?
3
votes
2answers
199 views
Standard errors for covariance estimate in R
This is a very simple question: how does one get the standard error for the covariance estimate in R? I estimate the covariance using the cov function but there ...
1
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0answers
88 views
Merge covariance matrices
I have two 2x2 covariance matrices, stemming from bivariate datasets that are approximately normally distributed. I want to create a mixture distribution and for that I need to merge the covariance ...
