1.030 covariance questions.

analyzing residuals vs. fitting a full model

In my field, some scientists look for relationships between a dependent variable, y and a covariate, x1, while controlling for a ...

I am using the statsmodel.ols module to compute an omnibus (ANOVA) F-test for three within-subjects factors; 2*3*2 levels design. The Cond. No. of the omnibus test (...

23 Is a sample covariance matrix always symmetric and positive definite?

4 answers, 25.627 views sampling covariance
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 ...

1 given $Z_i ~ N(0,1)$ and $Z^2 = Z_1^2 + Z_2^2$ what is $Cov(Z^2,Z_1)$?

1 answers, 27 views expected-value covariance
Currently I am at the stage where: $Cov(Z^2,Z_1) = E(Z^2*Z_1) - E(Z^2)E(Z_1)$ $=E(Z^2*Z_1)$, because expectations of normal, or combination of normal variables is zero. After this I have no idea ...

Confusion about asymptotic properties of Yule-Walker estimator

0 answers, 12 views time-series covariance asymptotics
The Yule-Walker estimator of an AR(1) process has some well-known asymptotic properties ... except there are TWO results governing these properties. I am not sure which one to use? The first result ...

2 Outlier and correlation

2 answers, 53 views correlation variance covariance outliers
Hi, I have a question. The scatter plot doesn't show any type of correlation and there is an outlier. If the outlier was to be removed, would the correlation: Increase dramatically Increase ...

19 Simulating time-series given power and cross spectral densities

I am having trouble generating a set of stationary colored time-series, given the covariance matrix (their PSDs and CSDs). I know that, given two time-series $y_{I}(t)$ and $y_{J}(t)$, I can ...

10 How to do factor analysis when the covariance matrix is not positive definite?

I have a data set that consists of 717 observations (rows) which are described by 33 variables (columns). The data are standardized by z-scoring all the variables. No two variables are linearly ...

Taking M samples with replacement from N options, what is the covariance?

Suppose that you take $M$ samples with replacement from numbers $\{1,2,..., N\}$. Denote the number of time each number is sampled by $\{K_1, ..., K_N\}$. Is it possible to say something about the ...

2 Prove positivity of chi-squared statistic with general covariance matrix

For a "simple" chi-squared test statistic $\chi^2 = \sum_i (x_i - \mu_i)^2 / \sigma^2$, it's clear that the domain is positive since both the numerator and denominator of every term in the sum over ...

Covariance of random variables whose sum is less than a constant

Suppose that we have integer random variables $X>0$ and $Y>0$ and constant number $a$. We have: $X+Y < a$. Can we say that the covariance of these random variables is less than or equal to ...

generating correlated samples

let's say I have n correlated variables, from which I would like to sample. I know there are several packages, like mvrnorm, ...

Individual data point variance and covariance

In the paper, "Data analysis recipes: Fitting a model to data" (Hogg, Bovy, Lang), individual data point variances are found and used for subsequent statistical analysis. The data and corresponding ...

2 Correlation matrix for multivariate Cauchy distribution

I have found an equation for the entropy of a $p$-variate Cauchy distribution here [page 70]: $H(X,R) = \frac{1}{2}\log(\det(R))+f(p)\,,$ where $X=(X_1,X_2,\dots,X_p)$ is vector of random variables ...

3 Can the correlation or covariance of two variables be translated into a probability distribution? [closed]

Question: Can the correlation coefficient (r or r²) or the covariance (Cov(X,Y)) be somehow translated into a probability distribution for the dependent variable? Example: If r²=0.8 for two random ...

1 Why is distance covariance defined squared, while covariance is not?

I am dealing in a data science project with correlation analyses using pearson and distance correlation. While trying to understand the differences between them, I learned about the differences by ...

1 Is the covariance matrix a diagonal matrix with variances on the diagonals?

I am a geophysicist learning about geophysical inverse problems. In many papers, the authors discuss the "covariance matrix" as it applies to the inverse problem. In most geophysical applications, ...

A non-ANCOVA situation for correcting slope heterogeneity with a covariate

0 answers, 15 views regression covariance heterogeneity
I have a statistics problem than I have spent hours trying to tackle with no success. I know what I want to test, I just can't figure out what the method is. I am looking at the relationship of ...

1 If one dimension of the data is scaled by a factor, how would it affect the probability of the Gaussian distribution?

I have fitted a maximum likelihood Gaussian distribution $N(\mu, \Sigma)$ on a multidimensional data set $X$. I wonder how would $p(X)$ change if one dimension of $X$ is scaled by a factor? It's ...

What do “scales” refer to when comparing correlation matrix to covariance matrix?

1 answers, 29 views correlation covariance units
In one post it was written that: You tend to use the covariance matrix when the variable scales are similar and the correlation matrix when variables are on different scales. What does scale ...

6 Principal Components of Random Walk

1 answers, 77 views pca covariance random-walk
In this blog figure 4 shows that the principal components of a random walk are sinusoidal with increasing frequency for decreasing eigenvalue. Is there an intuitive way of understanding this? If I ...

1 Calculating the covariance between 2 ratios (random variables)

I am a little stuck with my project. In the calculations of my project, I need to calculate the spread of some random variables. Up to now, there was no special difficulty to analytically calculate ...

5 Covariance of a compound distribution

I am trying to find the covariance of a compound distribution. Given $X=x$, where $X \sim \mathrm{Uniform}(0,1)$, $Y$ is (conditionally) normally distributed with mean $x$ and variance $x^2$. I ...

Covariance between a variable and a non-linear transformation of it

1 answers, 22 views random-variable covariance iid
Suppose $\epsilon \overset{\text{iid}}{\sim} N(0, \sigma^2)$ Can we make any assumptions about Cov$(\epsilon, \frac{\epsilon^2}{1 + \epsilon^2})$?

3 How many samples are needed to estimate a p-dimensional covariance matrix?

3 answers, 1.888 views mathematical-statistics covariance
In general, how many points are needed to estimate a p-dimensional covariance matrix? Does it depend on how the data are spread out across the different dimensions? Does it depend on the true ...

1 Online weighted covariance

1 answers, 506 views python covariance online
I'm trying to calculate a covariance matrix using weighted data in a single pass, and I'm not sure that I'm doing it correctly. I found a wikipedia article which gave the following python* code:<...

51 How and why do normalization and feature scaling work?

I see that lots of machine learning algorithms work better with mean cancellation and covariance equalization. For example, Neural Networks tend to converge faster, and K-Means generally gives better ...