# Questions tagged [random-vector]

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### If $X$ and $Y$ are independent random vectors, is $X_{i}|X_{i-}$ and $Y_{i}|Y_{i-}$ independent?

Given $X$ and $Y$ are independent random vectors, would $X_i|X_{i-}$ be independent of $Y_{i}|Y_{i-}$? Where $i-$ contains elements of the random vector not present in $i$. Basically what I want to ...
• 143
208 views

### Regression and independent random vectors

Lets consider that data samples are generated from random vectors $(X_1, Y_1)...(X_N, Y_N)$ of cross-sectional data. For regression one usually assumes that the error distribution is I.I.D. normally ...
• 143
1 vote
49 views

### Are moduli of components of Fourier transformed Gaussian random vector still independent?

Suppose $X=[X_1,\ldots, X_n]^T$ is a random (column) vector such that: $X_i \stackrel{i.i.d}{\sim} \mathcal{N}(0,\sigma^2), \ 1 \le i \le n$ $\mathcal{F} \in \mathbb{C}^{n \times n}$ is the discrete ...
182 views

### Representation of two Gaussian vectors as sums of independent Gaussian vectors

I know that if we have 1-dimensional Gaussian r.v. X and Y we can find coefficients $a,b$ so that $$X=aY+bZ+E[X-Y]$$ where $Y , Z$ are independent and $Z$ is standard Gaussian. Can we do something ...
• 21
1 vote
191 views

### Multivariate Log-Normal variables with given covariance

Given a symmetric positive definite matrix $\bf \Sigma \in \mathbb{R}^{n \times n}$, I want to find a matrix ${\bf \Gamma} \in \mathbb{R}^{n \times n}$ and a vector ${\bf m} \in \mathbb{R}^n$ such ...
163 views

### What does it mean for a sequence of random vectors to converge to a random vector?

I am reading about convergence of random variables from Wikipedia and I come across this. Note that the condition that $Y_n$ converges to a constant is important, if it were to converge to a random ...
• 2,603
1 vote