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Tagged with sum covariance
8
questions
2
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1
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323
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R function to compute variance of average of correlated random variables
I want to calculate the variance of the average of n correlated variables. I found a formula for that in Borenstein et al. (2009) Introduction to Meta-Analysis.
$$\operatorname{Var}\left(\frac{1}{m}\...
- 151
1
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1
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Fast Evaluation of a Double Sum
Let
$q$ be a probability distribution on $\mathcal{X}$,
$w$ be a nonnegative function from $\mathcal{X}$ to $\mathbf{R}$ which is bounded away from $0$ and $\infty$, and
$s$ be a bounded function ...
- 1,346
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1
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How can we decompose $\text{Var}[\sum_{i=1}^n\sum_{j=1}^m f(A_i,B_j)]$?
Formulas for decomposing the variance of a summation of random variables can be found on Wikipedia but what is the variance of a double summation of a function of random variables? That is, are there ...
- 795
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Linear regression $y_i=\beta_0 + \beta_1x_i + \epsilon_i$ covariance between $\bar{y}$ and $\hat{\beta}_1$
I am currently reading through slides from Georgia Tech on linear regression and came across a section that has confused me. It states for
$$
y_i=\beta_0+\beta_1x_i+\epsilon_i
$$
where $\epsilon_i \...
- 367
1
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2
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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 ...
- 286
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882
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Correlation between Weighted Sum of Random Variables and Individual Random Variables
Given the following set of random variables and constants,
$\newcommand{\inreala}[2]{\in \mathbb{R}^{#1 \times #2}}
\newcommand{\var}{\mathrm{Var}}
\newcommand{\cov}{\mathrm{Cov}}
\newcommand{\corr}{\...
- 134
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covariance between sum and elements of sum, given the weighting of the elements, their variances and the covariance between elements
For simplicity let's say that M consists out of two elements: A and B.
The weighting of A is w(A) and of B it is w(B). Hence w(A)+w(B)=1.
Both weightings are given. Also given is Var(A), Var(B) and ...
- 11
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2
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8k
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What is the variance of the sum of Yi's
Seems a simple enough question, and I presume that, if Yi are normally distributed,
Var(Sum(Yi)) = Sum(Var(Yi))
This feels like I'm jumping to the wrong conclusion though.
Any help would be ...
- 31