The Stack Overflow podcast is back! Listen to an interview with our new CEO.

Questions tagged [covariance]

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.

1,158 questions
Filter by
Sorted by
Tagged with
36 views

When covariance matrix will be identical to the correlation matrix [on hold]

Under what conditions will the covariance matrix ∑ be identical to the correlation matrix, whose (i, j ) entry gives the correlation between attributes Xi and Xj ?
17 views

Prove stationarity

It can be easy question, but it is a part of bigger exercise. I have problem with lack of statement "uncorrelated" Prove that if ${X_t,t \in T}$ is stationary, then $Y_t = X_t - X_{t-1}$ is also ...
397 views

Proof that if covariance is zero then there is no linear relationship

I get that a zero covariance doesn´t imply independence, but everybody says that if there is dependence and the covariance is zero then it is a non linear dependence. People base their interpretation ...
32 views

17 views

Covariance Matrix (Long/Short Portfolio; Different Weightings)

I am attempting to calculate the expected one-day standard deviation of a portfolio in dollars. In other words, I am looking for the following: "I expect my portfolio to move _______ dollars on ...
14 views

21 views

logic of autocovariance in time series

I am confused with the “autocovariance” in time series. In textbooks it says that it: “measures the linear dependence between two points on the same series observed at different times”. Why “two ...
20 views

Linear model fitting with covariance, by group

I need to fit a linear model to a percent change value over time (categorical), for grouped data and need to include age covariance. I've tried to work with these models: ...
7 views

Should you correct for group characteristics that are correlated to group membership

A little over a year ago, we have collected data by administering neurpsychological tests in several prisons (n=280). While this data is interesting by itself, we would like to compare these scores ...
36 views

24 views

Interpreting predictive models in the presence of omitted variables

Suppose the best predictive model from a set of possible models is a univariable model, due to lots of moderate correlations with other variables for example. However, if I use this model for ...
12 views

De-standardizing covariance matrices after applying PCA?

If I decide to use PCA to estimate a high-dimensional asset portfolio covariance matrix using reduced dimensions, I can use the following procedure to transform the low-dimensional matrix back to the ...
40 views

covariance between continuous and discrete random variables

Let $Y \sim Ber(p)$ and $X \sim N(\mu,\sigma^2)$. I want to compute $Cov(Y,X)$ and joint distribution of $(Y,X)$. Are there any useful reference? Thanks.
22 views

If two lognormal distributions have correlation $\rho$, what is the correlation between the log of those distributions?

Suppose I have $X,Y$ which are lognormal with correlation, $\rho$, what is the correlation between $log(X)$ and $log(Y)$? I tried working it out analytically and I'm getting that you have to ...
59 views

Can you use Kendall's Tau to compute covariance matrix?

I am working with multivariate archimedean copulas, and I am wondering how I can extract a covariance matrix out of them? I can get Kendall's Tau matrix of correlation so I was thinking that maybe I ...
17 views

96 views

Are the conditional expectation values of y and f necessarily equivalent in Gaussian processes?

Suppose $y$ is a Gaussian process given by $y \sim f + \epsilon$, where $\epsilon$ is a Gaussian noise model with zero mean, and $f$ is a deterministic yet unknown mean function (or a Gaussian process ...
26 views

Proof that covariance of RV and group average is less than variance of RV

I have a random variable $X_i$ and a group of $N_j$ other random variables that includes $X_i$. Let's just call this group $J$. There are no distributional assumptions made on these RVs (other than ...
34 views

How to make a scree plot out of SVD data to validate PCA

After doing a singular value decomposition (SVD) of a data set, I'm left with three matrices: 1. An orthogonal Left Singular Vector (U) 2. diagonal matrix with elements in descending order (S) 3. ...
24 views

Recently, I am reading Peter J. Bickel's paper Regularized Estimation of Large Covariance Matrices. In that paper, the author tries to prove lemma A.3, which goes as follows: Let $Z_{i}$ be i.i.d. $\... 3answers 44 views In a repeated measures model where assessments are performed over time, should baseline data be excluded if baseline covariate is used? In a model where subjects are evaluated over time and a baseline (time=0) covariate is used (eg, ... 0answers 12 views How does a covariance intensity function measure clustering? I was taught in a class on spatial statistics that the covariance intensity function (defined below) measured clustering and inhibition in a point process, but isn't used because good test statistics ... 0answers 8 views Moderation and Ancova I conducted a repeated measures anova with accent (British versus American) as 1 level and dress style (business, super casual, and business casual). My dv was how professional each was rated (1 to 7).... 2answers 98 views Covariance between two binomial random variables Consider a binomial random variable$X$with parameter$p$and another binomial random variable$Y$with parameter$q$. What is the covariance of$X$and$Y$? How well does the proof generalize to$n$... 0answers 28 views What statistic to use in testing the variance of maximum likelihood estimators (A physicist self-studying statistics here) I was previously confused about the meaning of the standard error in a maximum likelihood estimate. Certain stack exchange posts (linked below) have gone ... 0answers 27 views the accuracy of covariance between two high-dimensional vectors Question Is the covariance between high-dimensional vectors less accruate than covariance between two vectors in low-dimensional vecotrs? I am asking this questio to check if there is a need for '... 0answers 13 views Covariance correction for linearly mixed signals Consider the simple linear mixing model: $$X = AS + v$$ where:$X$is N-by-T,$A$is N-by-M,$S$is M-by-T, and noise$v\sim\mathcal{N}(0,\Sigma_v)$. Assume that we know the matrices$X, A,...
I read in a textbook (Japanese one) that the spherical covariance function is only valid for dimensions $d = 1,$ $2,$ and $3.$ I have the following questions: Does that mean the spherical covariance ...