# Questions tagged [covariance]

Questions about covariance, a measure of (linear) association between two random variables.

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### Decomposition of order 3 tensor symmetric along two dimensions

I have a 3rd order tensor $\mathbf{A}$ consisting of symmetric covariance matrices (with dimensions of space by space) stacked in time. I would like to compute the leading spatial features that ...
• 89
1 vote
7 views

### 2D Kernel for Gausian Process Regression

I want to use Gaussion Process Regression to fit a function to data. Since I know a little about the target function, I would like to build a suitable kernel from existing kernels. The input vector ...
1 vote
12 views

### Graphical model - log transformed covariance matrix

It is known that the non-zero entries of the inverse covariance matrix constitute an estimate on the edges in a graphical model. I wonder if there is an analog or similar result for the log-...
• 824
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### Inverse transform of the exponential covariance function

Let $C(h)$ be the exponential covariance function, Bochner's theorem says that $C$ is positive definite if and only if its the Fourier transform with respect to a spectral measure $\chi$. Now, under ...
47 views

### Singular vectors from true and sample covariance do not align

Suppose we have a covariance matrix $C\in\mathbb{R}^{p\times p}$ which is diagonal with exponential decaying values. This covariance matrix is used to sample $n$ data points $x\sim\mathcal{N}(0,C)$ ...
1 vote
29 views

• 151
1 vote
31 views

### Is it possible that $A+A_{\text{off-diag}}\succ0$ , where $A\succneqq0$?

Denote $A_{\text{off-diag}}:=A-\text{diag}(A)$, i.e. setting diagonal elements to be zero. Denote $A\succneqq0$ iff $A$ is positive semidefinite (and not positive definite), while $A\succ0$ iff $A$ is ...
• 511
52 views

### Kendall's tau coefficent of Bivariate Normal [duplicate]

Let the joint distribution of (𝑿, 𝒀) be bivariate normal with mean vector $\begin{pmatrix} 0 \\ 0\end{pmatrix}$ and variance-covariance matrix $\begin{pmatrix} 1 & 𝝆 \\ 𝝆 & 1 \end{pmatrix}$...
• 53
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### Finite nonzero covariance but infinite variance

Cauchy-Schwarz tells us that it is not possible for random variables $X,Y$ to both have finite variance while having infinite covariance. Now it is easy to think of examples where $X,Y$ have zero ...
• 7,896
16 views

### Transformation step in lag-$l$ autocovariance for linear time series that I can not understand.

We have a linear time series defined as follows: $r_t=\mu+\sum_{i=0}^{\infty}\psi_ia_{t-i}$, where {$a_t$} is a sequence of iid random variables with mean zero and a well-defined dsitribution. The lag-...
• 137
22 views

### Comparing distributions of binary valued vectors: covariance matrix is enough?

Say we have two discrete distributions, $\vec{y}\sim p_y$ and $\vec{x}\sim p_x$, for both of which, data vectors have binary-valued entries: $\vec{y}\in\{0,1\}^n$ $\vec{x}\in\{0,1\}^n$, where $n$ is ...
• 43
### Is true that $\operatorname{Var}(X|Y)=\operatorname{Var}(X-E[X|Y])$? [closed]
Is true that $\operatorname{Var}(X|Y)=\operatorname{Var}\left(X-E[X|Y]\right)$? Also, is true that $\operatorname{Cov}\left(E[X|Z],E[Y|X]\right)=0?$
### Calculating $Cov\left(\overline{Y}_j,\:\overline{Y}\right)$ for a basic one-way model
Consider the basic one-way model: I want to show that $Cov\left(\overline{Y}_j,\:\overline{Y}\right)=\frac{\sigma ^2}{na}$. I derived the following expected values: E\left(\overline{Y}_j\right)=\mu ...