0 covariance questions.

6 Unsure if this derivation for covariance function is valid?

I have a stochastic process (Ornstein-Uhlenbeck) defined as: $X(t) = e^{-at}(\int_0^t e^{a \tau} dW(\tau) + X_0)$ Where $W(t)$ is the Wiener process, and $X_0$ is the initial value of my process. I ...

1 principal component analysis or factor analysis to be used with qualitative data

I want to make a model in which the dependent variable is nutritional levels of children, for this, I calculated $z$ scores like weight for ...

1 Correlation in least square estimator k-fold cross validation

I have model $$Y = \beta + \epsilon$$ where $Y$ is scalar and $\beta \in \mathbb{R}$. $\epsilon$ has mean $0$ and variance $\sigma^2$. If I perform a k-fold cross validation, what is the ...

2 Does the magnitude of covariance have any real meaning? [duplicate]

I am not able to understand logic behind coming up with this formula for covariance. We know that the sample covariance formula is: $${\rm Cov}(x,y)=\frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{n-1}$$ ...

1 Online weighted covariance

1 answers, 365 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:<...

1 Arrange features in a table that minimizes covariance

I have a dataset of vectors represented by a $n_{rows} \times n_{cols}$ matrix $M$. Each row is a vector and each column is a feature. There are $n_{cols} = n \times n$ features. We use the sample ...

3 Cov(X,Y) when X is a binary variable [duplicate]

Say we have a random variable $Y$ which is positive, and a binary variable $X$, i.e. takes values 0 and 1 only. I have seen (in various places) that: $$Cov(X,Y) = E[Y | X = 1| - E[Y | X = 0|$$ How ...

1 Co-variance of a sum with one variable appearing twice

1 answers, 30 views variance covariance
I am interested in the co-variance of two joint coefficients, with one variable appearing in either joint coefficient, i.e. $\mathrm{Cov}[x+z,x+w]$. But let me start with my model, let's say I want ...

1 Uncorrelated/orthogonal random vectors

0 answers, 284 views correlation random-variable covariance
For random variables $X,Y\in\mathbb{R}$ we say that they are orthogonal if $E(XY)=0$ and uncorrelated if $E((X-E(X))(Y-E(Y))=0$. In what follows I assume all random variables to be centered so ...

multiple regression derivation of betas in terms of covariance/variance [duplicate]

In simple linear regression $y=\beta_0+\beta_1x$, you the least square estimator $\hat\beta_1=\frac{\sum(x_i-\bar x)(y_i-\bar y)}{\sum(x_i-\bar x)^2}$ can also be represented as \$\hat\beta_1=\frac{cov(...