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.

learn more… | top users | synonyms

1
vote
0answers
11 views

How to test the significance of covariance?

I'm using the Mutual Informacion covariance in RNA sequences and I want to know if there exits a way to test if some covariance is significant, let's say, an associated p-value. Thanks to all for ...
0
votes
0answers
7 views

Sub-space / latent-space covariance

I am not entirely sure what I should be googling for this in my present context. Basically I am working with a set of latent variable models such as the Gaussian Processes latent variable model ...
0
votes
0answers
8 views

Covariance function to draw an inverse function

In a Gaussian Process (GP), we know that choice of the covariance function determines the shape of function that can be drawn from the GP. eg. Constant : $\sigma _{o}^{2}$ Draws constant function ...
3
votes
1answer
31 views

Why is pure sample covariance a bad metric to understand the degree of correlation between two variables?

Covariance helps you understand how variables are linearly related. Would it be possible to have two pairs of variables in a deterministic relationship (i.e. linearly correlated variables) that have ...
0
votes
0answers
9 views

variance of data of correlated poisson means?

I want to find the mean and standard deviation for the data for the following question. We have 10 houses of known different sizes. The number of people living per square meter has a poisson ...
0
votes
0answers
10 views

Econometrics 2: Covariance (xt, xt+1) in Moving Average process of order 1,

Could you help me to show that if X(t+1)=e(t+1)+alpha(1)*e(t), Then Cov[x(t), x(t+1)]=alpha(1)*Var[e(t)] Thank you very much, your help is appreciated
2
votes
0answers
32 views

Asymptotic distribution of $\hat{B_1}$in simple linear regression

I am currently studying how to $\bf{identify}$ the parameter $B_1$ in a simple univariate regression model where we have $Y=B_0+B_1X+\epsilon$ with the usual assumption of $X$ being exogenous, ...
0
votes
1answer
32 views

Linear regression coefficients from covariance matrix [duplicate]

In case of two random variables $y,x$ we have that the best linear fit $y = \beta x + \epsilon$ satisfies $$ \beta = \frac{\mathrm{Cov}(x,y)}{\mathrm{Cov}(x,x)}. $$ That is, if I known covariance ...
1
vote
0answers
16 views

Loss function for rank deficient covariance matrices?

I'm trying to compare the efficiency of different estimators of the covariance matrix of a particular type of multivariate normally distributed data. This comparison, as well as the estimation process ...
2
votes
1answer
48 views

How do I generate two correlated Poisson random variables?

How would I simulate observations from a bivariate Poisson distribution such that they have a nonzero covariance? The hint I was given is that I need to use the fact that the sum of two Poisson random ...
-1
votes
0answers
22 views

Expectation of product of random variables whose covariance is unknown

Is it possible to compute $\mathbb{E}[XY]$ where $X \sim \mathcal{N}(\mu_X, \sigma_X^2)$ and $Y \sim \mathcal{N}(\mu_Y, \sigma_Y^2)$ if $\mbox{cov}(X,Y) = \sigma_{XY}$ is unknown? My intuition tells ...
2
votes
1answer
42 views

Covariance of natural logarithms — how to estimate $\sigma (\mathbf X, \mathbf Y)$ from $\sigma (\ln{\mathbf {(X)}},\ln{\mathbf {(Y)}})$?

I have $$\operatorname{Cov} (f{\mathbf {(X)}},f{\mathbf {(Y)}})$$ where $\operatorname{Cov}$ denotes the covariance and $f(\mathbf X)$ is a nonlinear function, i.e. $f(\mathbf X) = \ln(\mathbf X)$. ...
0
votes
1answer
21 views

Mixed model analysis: random vs repeated statement

I have data from a longitudinal parallel groups study where there are 46 subjects randomized to 1 of 5 treatment groups, each subject with roughly 13 observations over time on a given outcome measure. ...
0
votes
0answers
13 views

How to get covariance matrix of the coefficient estimates of compound regression model in SPSS

AFter running regression model in SPSS, I get the compound model: ln(diamter)=1.126*height +3.102. I would like to have the covariance matrix of the coefficient estimates of this model and get the ...
4
votes
0answers
86 views

Caclulating standard errors for generalized least squares without raw data (just sample means and covariance)

I have a question very similar to the question asked here: is it possible to calculate standard errors (specifically, the standard error of the intercept) for generalized least squares regression ...
3
votes
1answer
78 views

Show that $\widehat{Cov(\hat{\mu},Z_i)}$ is always zero even $Cov(\mu,Z_i)$ is not always $0$

I will state the question first then my work. Q: We have a regression model, $Y_i=\beta_0+\beta_1X_i+\mu_i$ where $Cov(\mu_i,X_i)=0$ is not guaranteed. Suppose that $Z_i$ is an instrumental ...
4
votes
1answer
87 views

centering two variables X and Z makes cov (X,XZ) = 0

I've read that centering two normal (or symmetrical) variables $X$ and $Z$ affects correlation of centered $X$ with interaction term $X\cdot Z$ in such way, that this correlation $cor(X-EX, X\cdot Z)$ ...
-1
votes
0answers
18 views

Conditional Density Formula (using Gaussian copula)

Is it true that $R_k$ can be calculated using Pearson correlation, Spearman's $\rho$ or Kendall’s $\tau$? And is it true that If we use Pearson correlation, then the correlation(covariance) $R_k$ in ...
3
votes
1answer
75 views

Show that the sample covariance converges in probability to the $Cov(X,Y)$

Suppose we are given $[(Y_i,X_i)]^{n}_{i=1}$ which is a random sample from the joint distribution of $(Y,X). Show that the sample covariance converges in probability to the $Cov(X,Y)$ My thought ...
1
vote
3answers
118 views

Covariance greater than Variance?

It is straightforward to verify that for two random variables $X$ and $Y$ with variances $\sigma^2_X \neq \sigma^2_Y$, we have that $$\Big|{\rm Cov}(X, Y)\Big| \leq \max\{\sigma^2_X,\, \sigma^2_Y\}$$ ...
4
votes
2answers
65 views

If $E[Y|X]=a$ for some constant $a\neq 0$, then does $cov(X,Y)=0$?

I'm currently working on the following problem: Q: If $E[Y|X]=a$ for some constant $a\neq 0$, then does $cov(X,Y)=0$? Now I am quite lost as to how to do this problem as the question does not ...
1
vote
1answer
41 views

Gaussian Process: Using partitions of a Cholesky decomposition solution for conditional deduction

If I define a GP over observed values, $y$, of a sensor reading over time, $t$, as (for simplicity assuming discrete time series e.g lets say readings after every 5 mins) : $y=f(t)+\epsilon$ where ...
0
votes
0answers
14 views

Find the bounding rectangle of a covariance matrix based on mahalanobis distance

I'm trying to develop an algorithm that makes use of the Mahalanobis distance from an arbitrary test point to assign a score to each observation in a dataset. I want to only consider observations ...
1
vote
1answer
40 views

Posterior covariance from GPML toolbox

I am currently using the GPML toolbox to perform regression. Generally, after learning the hyperparameters we can extract the posterior mean and variance by using the function in the toolbox as ...
0
votes
0answers
19 views

Analyze estimated noise covariance matrix

In image processing, an algorithm was created for the simultaneous Bayesian estimation of the unknown correlated noise covariance matrix. How can it be proven that the mean of the computed estimates ...
3
votes
0answers
49 views

effects of Box-Cox transformation on covariance

I'm trying to synthesize data for a Monte Carlo simulation. I have a stationary random process $x$ and can readily estimate its covariance matrix $S$. I know that if the increments of the process are ...
3
votes
1answer
60 views

Examples of marginal independence, conditional dependence

I am interested in finding "real-world" examples of when variables might exhibit marginal independence but are conditionally dependent given some other variable. It seems to me that the converse ...
3
votes
1answer
79 views

Find the expectation and covariance of a stochastic process

The problem is: Let $W(t)$, $t ≥ 0$, be a standard Wiener process. Define a new stochastic process $Z(t)$ as $Z(t)=e^{W(t)-(1/2)\cdot t}$, $t≥ 0$. Show that $\mathbb{E}[Z(t)] = 1$ and use this result ...
3
votes
1answer
29 views

Question regarding covariance

I'm trying to prove a theorem, where it is given that each $X_i$ is independent and identically distributed with mean $\mu$ and variance $\sigma^2$. Within this theorem, I have multiple sub-results to ...
1
vote
1answer
38 views

What is the asymptotic covariance matrix?

Is it true that the asymptotic covariance matrix is equal to the covariance matrix of parameter estimates? If not, what is it? And what is the difference between the covariance matrix and the ...
3
votes
1answer
43 views

Expectation of covariance in derivation of Kalman filter

I'm working through the derivation of the Kalman filter equations from this paper (or alternative source here) and I'm unsure of the derivation of the state prediction covariance (equation 2 in the ...
2
votes
1answer
45 views

Example of dependence with zero covariance

This is a constructivist question. Please provide a bi-variate distribution or density/mass function of two absolutely continuous/discrete (but not mixed-type) random variables, which (may) have ...
-1
votes
1answer
38 views

partitioning variances, higher order products and multivariate skewness

If A,B and C all contribute to Z as: $$ Z = A*B*C $$ we can get the contributions of ABC to the variance in Z as: $$ Var(Z) = Var(ABC) $$ getting independent contributions of A, B and C and ...
1
vote
2answers
71 views

Is covariance between two dummy variables zero?

Here is a problem I am facing: I need to test a hypothesis (t test), the formula for which is $t = \frac{\hat{B_1} - \hat{B_2}}{se(\hat{B_1} -\hat{B_2})}$ Now, we know that the bottom isnt actually ...
0
votes
0answers
25 views

Meta analysis on multiple endpoints and unknown covariance

I am doing meta-analysis on intervention studies on human subjects where a number of measures were obtained before and after the intervention in a treatment and a control group. We categorize the ...
0
votes
0answers
60 views

Hayashi yoshida estimator for correlation not coming between -1 to 1

I took two time series data with 141 data points in total with time stamps. i found out actual correlation between them which is about 0.97. Now i find the Hayashi Yoshida estimator for correlation. ...
1
vote
0answers
77 views

Covariance of the empirical distribution function

Let $X_1, \dots, X_n$ be iid with cdf $F$. Let $\hat{F}(x) = \frac{\sum I(X_i \leq x)}{n}$ be the empirical distribution function. Suppose $x < y$ and compute $Cov(\hat{F}(x),\hat{F}(y))$. This is ...
1
vote
0answers
40 views

Calculating expectation function and covariance function

Let $E_n(t)$ denote the empirical cdf based on iid uniform $u[0,1]$ random variables $U_1,...,U_n.$ The corresponding uniform empirical process $(e_n(t),0\leq t\leq 1)$ is given by ...
1
vote
0answers
18 views

How to normalize by the covariance matrix? [duplicate]

I am trying to understand an image processing research paper [1] that calls for normalizing a distance between an object's center point and the center of a cluster of points by the covariance matrix ...
0
votes
1answer
116 views

What is the correlation between X and X+Y?

If $X$ and $Y$ are two random variables, how do I calculate the correlation of $X$ and $X+Y$ in terms of $\rho$, $σ_x^2$ and $σ_y^2$ given that the $\text{Variance}(X)= σ_x^2$ and ...
3
votes
1answer
153 views

Clarification: The covariance of intercept and slope in simple linear regression?

Help me understand this relatively simple (I think) concept: The covariance of the intercept ($\beta_0$) and the slope ($\beta_1$) in simple linear regression. Furthermore, what range of values ...
1
vote
1answer
57 views

Regression: Covariance table in spss vs. mplus

I want to use regression output (b, se B and cov of several predictors) as input for a new analysis. One example: I want to compute: SE^2(b1) + SE^2(b2) + 2 COV (b1,b2). If I do a basic regression ...
2
votes
2answers
33 views

Direct parametrization of Cholesky decomposition of spatial covariance matrix

In spatial data analysis, a simple way to model the covariance stucture between spatial observations is via a covariance function like $cov(y_i,y_j) = C e^{-rD_{ij}}$, based on some (euclidean) ...
7
votes
2answers
235 views

Expected value of a product of two compound Poisson processes

I'm working on my master thesis now and I've been struggling with a problem for some while now and no one seems to be able to help me or point me in any direction. So now I reach out to see if someone ...
4
votes
0answers
46 views

How do I solve this stochastic differential equation?

So I have a second order stationary process $Y(t), \infty < t < \infty$ which has a continuous sample function, mean $\mu_Y = 1$ and covariance function $r_Y(t) = e^{-|t|}, -\infty < t < ...
2
votes
1answer
42 views

In a two equation system, what is the meaning of the assumption “exogenous X is uncorrelated with ε1ε2”

Assume a triangular system such as \begin{eqnarray*} Y = X'\beta_1 + D\gamma_1 + \varepsilon_1 \\ D = X'\beta_2 + \varepsilon_2 \end{eqnarray*} with $Y$ and $D$ as observed endogenous variables, $X$ ...
0
votes
0answers
33 views

Fisher information matrix with negative eigenvalues, fix through singular value decomposition?

I have the following Fisher information matrix (just an example): ...
0
votes
1answer
24 views

minimizer weighted linear regression

In a regression problem, with $y=X\theta+\epsilon$ and $X$ is an $n$ by $p$ matrix the ‘weighted least squares estimate is the minimizer $\theta^{*}$ of ...
4
votes
1answer
129 views

(Co)variance of product of a random scalar and a random vector

Given a random scalar $ x \in \mathbb{R} $ and a random vector $ Y \in \mathbb{R}^n $ that are independent, can it be said that: $$ {\rm cov}(xY) = {\rm var}(x){\rm cov}(Y) + {\rm var}(x)E[Y]E[Y]^T + ...
0
votes
2answers
94 views

Why does the density function has product of variance and covariance for higher model order time series

In my previous question Density function for AR model, the density function of AR model has the covariance-variance matrix given as $\sigma^2 *V_p$. In multivariate Gaussian distribution, the pdf ...