All Questions
Tagged with mathematical-statistics covariance
130
questions
3
votes
1
answer
82
views
If $A^2$, and $B^2$ are DEPENDENT random variables, will $A$, and $B$ be necessarily DEPENDENT too?
I know that if $A$, and $B$ are independent, the independence is preserved for $A^c$, and $B^c$, where $c$ is a constant. I am wondering if the same applies to the case where the random variables are ...
- 31
0
votes
0
answers
19
views
Conditions of the covariance matrix between discrete and continuous variables
Does the covariance matrix for a discrete variable and a set of continuous variables have extra constraints beyond being positive semi-definite as in the case of a real-valued random vector?
...
- 336
1
vote
0
answers
17
views
Covariance calculation in a DiD estimation
I am estimating a difference-in-difference model estimating the effect of a parental leave reform on female wages. It is not possible to take the logarithm of the varaibles as a lot of wages are 0.
I ...
- 65
1
vote
1
answer
68
views
Proof of general linear process autocovariance
I am struggling to get to the general formula of the general linear process autocovariance.
If $Y_t = \mu + \sum_{k=0}^\infty \omega_k e_{t-k}$ where $e \sim WN(0,\sigma_e^2)$ (a.k.a. the general ...
8
votes
2
answers
215
views
Is there a simpler proof than mine for this obvious proposition about correlations?
$\newcommand{\e}{\operatorname E}$"Obviously" if $g$ is a weakly increasing function and $X$ and $g(X)$ are both random variables with finite variance, then the covariance (and hence the ...
- 10.5k
1
vote
0
answers
62
views
Ensemble mean of a fraction
I want to compute the ensemble mean of the term: $\frac{Y^2}{X}$
Both $X$ and $Y$ are random variables that are not independent. I want to compute $E[\frac{Y^2}{X}]$. I proceed as follows, (Using the ...
- 111
8
votes
1
answer
831
views
Covariance between sample mean and sample variance
I am trying to figure out the covariance between sample mean and sample variance from a population. We DO NOT know whether the population is normal (if it's normal, then the covariance is zero between ...
- 121
1
vote
1
answer
94
views
van der Vaart Asymptotic Statistics, page 38, why does $e_\theta'=\operatorname{Cov}_{\theta}t(X)$?
On Page 38 of van der Vaart's Asymptotic Statistics (near the bottom of the page), it says
By differentiating $E_\theta t(X)$ under the expectation sign (which is justified by the lemma), we see that ...
- 2,946
1
vote
0
answers
16
views
Need to come up with an equation or method to calculate a ratio between two arrays of numbers
I have two arrays of data:
# of Files
Time to Process in seconds
1
8
2
20
3
31
4
76
What I'm wanting to do is come up with an estimate of how long it will take to process n number of files. I ...
1
vote
1
answer
130
views
Covariance of two Random Variables
Suppose $r \geq 1$ distinct books are distributed at random among
$n \geq 3$ children.
(a) For each $j \in {0, 1, 2, . . . , r}$, compute the probability that
the first child gets exactly $j$ books.
(...
- 207
0
votes
0
answers
32
views
Variance of a linear combination of model predictions [duplicate]
I know that the variance of a linear combination of correlated random variables can be generalized (as in Variance of linear combinations of correlated random variables). My question has to do with ...
- 101
0
votes
1
answer
133
views
Correlation Between Min and Max of Two Different Uniform Distribution
$\textbf{This is a self-study problem that I am interested in knowing the correct answer.}$ $\textbf{However I do not trust my computations and I need help.}$
$Y$ is Uniform(0, 2); $Z$ is Uniform(1, 3)...
- 147
0
votes
0
answers
25
views
Can the idiosyncratic error term of a variable Y increase without the covariance of Y and X increasing?
If an outcome, variable $Y$, consists of a noise or idiosyncratic error ($e$) that is orthogonal to an independent variable, $X$, is it possible to increase $e$ without changing the $Cov(Y,X)$?
- 11
1
vote
0
answers
86
views
When would correlation between two variables not exist?
If we have two random variables $X$ and $Y$, then $\text{corr}(X,Y)=\dfrac{
\text{cov}(X,Y)
}{
\sqrt{
\text{var}(X)\text{var}(Y)
}
}$.
This correlation will not be defined if either variable has an ...
- 64.6k
0
votes
0
answers
27
views
Are measurements of a experiment scalars of Random Variables?
Random variable can be written as:
R = A + B
where
R - random variable
A - true value
B - error (also Random Variable)
Suppose now that ...
- 1