For questions about correlation of two random variables. Use it with [tag: random-variables] and [tag: probability].
2
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1answer
41 views
help understanding step in derivation of correlation coefficient
I'm looking to understand the starred step in the derivation below (also, if someone could help with the LaTex alignment, I'd appreciate it).
The regression line is $y= b_0 + b_1 x$, where $b_0$ and ...
0
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0answers
32 views
Correlation function of Brownian motion. What am I doing wrong?
Can anyone tell me where I am going wrong here? (I am leaving out any random fluctuation forcings, because I don't think they are relevant to my problem.)
1: $\displaystyle \frac{dv(t)}{dt}=-\eta ...
0
votes
0answers
13 views
What is a correct way to calculate the correlation of a phase?
To do a correlation or an autocorrelation of a magnitude or a complex number is straightforward. But what if you want to calculate the correlation of a phase? The problem being that, if your phases ...
1
vote
0answers
34 views
Calculation of conditional joint probability given certain conditionals for data which aren't independent
The context of this problem is the estimation of the distribution of a parameter $v$ given sets of data $A$ and $B$, where $A$ and $B$ are not independent.
Suppose I know $P(v | A)$ and $P(v | B)$. ...
0
votes
0answers
14 views
Calculating mean of data given correlated data pairs (how to apply Bayes theorem)?
Suppose that I have a data set of points $\{A_i\}$ and $\{B_i\}$. These data points are not independent, and the pairing is A1 <--> B1, A2 <--> B2 etc (i.e. the points come in pairs).
I want to ...
0
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0answers
14 views
Rebuild functions from Matrix(or any form) of unknown functions output
if I have a matrix that represent the output of several distinct functions, the output of every function is connected on the matrix (e.g.a11,a12 OR a11,a21-but not a11,a13)
-is there a way to ...
1
vote
1answer
48 views
correlation of product with its normally distributed factors
If x and y are normally dist. with standard deviation of 10%, and they are independent, then their product X.Y is 71% correlated with Y (or X).
I can show this empirically, but how to I prove it in ...
0
votes
2answers
47 views
Trying to understand correlation and independence geometrically
I am trying to understand correlation and independence of two random variables geometrically, but found it difficult to grasp the intuition and to explain it rigorously.
First, given two uniformly ...
2
votes
0answers
50 views
Dimension free Concentration bounds for Martingales
Consider the following random process which is defined on $n$ numbers $0\leq x_1,\ldots,x_n\leq 1$:
At each step, pick an arbitrary number, say $x_i$. Then randomly (and independently) change its ...
0
votes
0answers
21 views
Calculate the tendency of a set of samples [migrated]
I develop an application in which I constantly get samples of heart pulse.
I defined an interval of $t$ seconds.
In each $t$ seconds I have $n$ samples.
In every interval, I want to calculate the ...
2
votes
0answers
18 views
Finding the empirical correlation from a covariance matrix
I have this covariance matrix with five variables $X_1$ through $X_5$ in that order.
...
0
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0answers
21 views
Correlation question
I hope someone can help me with this:
Let $c(\rho)=\lim_{n\rightarrow\infty}n^{\alpha-1}\sum_{k=-(n-1)}^{n-1}\left[1-\frac{k}{n}\rho(k)\right]$ where $n=1,2,3,\ldots$, $\alpha\in(0,1)$ and $\rho$ is ...
1
vote
1answer
36 views
Random walk serial correlation
Given a model $$Y_t =b_0 + b_1 \cdot X_t + b_2 \cdot Z_t + e_t,$$ where the error term $e_t$ follows a random walk form of serial correlation $e_t = e_{t-1} + u_t$. Further assume $u_t$ has zero mean ...
1
vote
1answer
52 views
Inequality concerning the pairwise correlation coefficients of three random variables
I was asked to prove:
The correlation coefficients, $\rho_{12}$, $\rho_{23}$, $\rho_{13}$ between three random variables $X_1$, $X_2$, $X_3$ obey
...
0
votes
1answer
96 views
Covariance and Correlation
Suppose there were m married couples, but d of these 2m people have died. Regard the d deaths as striking the 2m people at random. Let X be the number of surviving couples.
Find:
a) E(X)
b) Var(X)
...
0
votes
1answer
41 views
Correlation of Indicator Variables
Show that for indicator random variables IA and IB of Events A and B:
Corr(IA, IB) = Corr(IAc, IBc) = -Corr(IA, IBc) = -Corr(IAc, IB)
Deduce that if A and B are positively dependent, then so are Ac ...
0
votes
0answers
43 views
Invariance of the correlation coefficient under linear transformations
Show that for arbitrary random variables X and Y, and constants a ,b ,c ,d with a and c nonzero, Corr(a*X+b, c*Y+d) = Corr(X,Y) if a and c have the same sign
= -Corr(X,Y) if a and c have opposite ...
2
votes
1answer
24 views
How can I mathematically show the similarity between these 3 plots?
I have 3 3D plots of field strength measured around an antenna.
I want to calculate the mathematical similarity between the points of the field patterns. How can I do this?
thanks
0
votes
0answers
23 views
Correlation coefficient, ACF,
In my book it says
$\rho_x(h) = \frac{\gamma_x(h)}{\gamma_x(0)}$, which is the definition of ACF, and $\gamma_x(\cdot)$ is the autocovariance.
It then should follow (under conditions of weak ...
0
votes
1answer
19 views
What values to choose for correlation?
To work out correlation I'm using the online calculator : http://easycalculation.com/statistics/correlation.php
...
0
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0answers
79 views
What do angle brackets ($\langle\rangle$ ) mean in mathematics/statistics (autocorrelations)?
Okay, so the logarithmic return on a stock is given by:
$$r_τ (t) = \ln P(t+τ) - \ln P(t),$$ where τ is the interval of time.
I have no problem calculating that. My question comes to the following ...
5
votes
1answer
129 views
Find $\operatorname{argmax}_x \operatorname{corr}(Ax, Bx)$ for vector $x$, matrices $A$ and $B$
This is similar to, but not the same as, canonical correlation: For $(n \times m)$ matrices $A$ and $B$, and unit vector $(m \times 1)$ $x$, is there a closed-form solution to maximize the correlation ...
0
votes
1answer
15 views
Correlation Based Filter
i found this paper. Im interesting in part 2.3 Feature Weighting.
The correlation function is known from wikipedia and almoast clear ( i can write a function to calculate the value :) )
But now i ...
0
votes
0answers
33 views
Probability Density Function and Eigenvalue Spectrum of Correlation Matrix
My question is in the link...
http://www.flickr.com/photos/88684900@N03/8654322505/in/photostream
0
votes
1answer
43 views
Is the relation of having positive covariance well behaved with respect to taking the inverse?
Let $X$ and $Y$ be two random variables, $X$ strictly positive. Assume that Cov$(X,Y)>0$. Does this imply that Cov$(1/X, Y)<0$?
I know that being positively correlated is not a transitive ...
0
votes
1answer
142 views
special matrix in terms of its covariance matrix
How can we find a matrix $S\in \mathcal{M}_{n,n}$ and $Z\in \mathcal{M}_{n,m}$ whose $n$ entries of the $i^{th}$ column $Z_i$ are correlated $Z_i \sim \mathcal{N}(0,S)$ where $S \in \mathcal{M}_{n,n}$ ...
3
votes
2answers
57 views
Covariance$(X,Y) \geq 0$ if $X,Y \geq 0$?
I was wondering if you can say something about the covariance of two positive variables $X$ and $Y$?
0
votes
0answers
58 views
Sum of correlated conditional variables
I have a normal random variable X with mean $\mu_x$ and variance $\sigma_x^2$. I take readings from only X every day (these observations are independent). I have another normal random variable Y ...
0
votes
1answer
23 views
How to correlate the timestamps of 2 systems?
Whenever I've done (simple) correlation in the past, I've always had 2 sets of data that had "connected" axes:
...
0
votes
0answers
35 views
Is the correlation function convex or not?
Suppose the function for statistical correlation is a non linear constraint in a non linear programming model:
$$
\frac{\sum_{t=1}^T (p_t - \bar{p})(R_t - \bar{R})}{\sqrt{\sum_{t=1}^T (p_t - ...
0
votes
1answer
45 views
What is the correlation function in multivariable/vectoral case?
I know that the correlation function between random variables $X$ and $Y$ is defined as
$$
\rho_{X,Y}=\mathrm{corr}(X,Y)={\mathrm{cov}(X,Y) \over \sigma_X \sigma_Y} ={E[(X-\mu_X)(Y-\mu_Y)] \over ...
1
vote
3answers
148 views
What is a direct correlation?
I have two contrary definitions of for the direct correlation between two variables $X$ and $Y$
Their correlation coefficient is close to $1$.
There is a direct causal relationship between the ...
0
votes
1answer
27 views
Normal distribution $\rho_{X,Y} = 0 \rightarrow X \bot Y$
Assume $X \sim \mathcal N(\mu_1, \sigma_1^2)$ and $Y \sim \mathcal N(\mu_2, \sigma_2^2)$. If $\rho_{X,Y} = 0$ then $X \bot Y$.
Can someone give a hint why this is true ?
1
vote
0answers
30 views
Sorting Vectors based on their correlation
This problem [question]: Sort vectors according to their distance between them is about sorting vectors based on the distance between them. What about sorting vectors based on the correlation ...
0
votes
1answer
44 views
The science of pearson product moment correlation coefficient
I need to compare two sound signals for similarity, I took cross-correlation of both the signals and I got a cross-correlation signal, now I intend to use pearson correlation coeff formula to get the ...
0
votes
1answer
105 views
Pearson Correlation Coefficient Interpretation
Let $X=(1,2,3,...,20)$. Suppose that $Y=(y_1,y_2,...,y_{20})$ with $y_i=x_i^2$ and $Z=(z_1,z_2,...,z_{20})$ with $z_i=e^{x_i}$. Pearson correlation coefficient is defined by formula
\begin{equation}
...
0
votes
1answer
54 views
correlation between two different variables
I am studying stochastic processes and found the next problem:
Let $A$ and $\Phi $ be two independent random variables such that $E(A) = 0$, $E(A^2) < \infty$, and $\Phi$ is uniformly distributed ...
0
votes
1answer
60 views
Intraclass correlations can be negative, yet they are a ratio of two variances (which are positive)
Estimates of intraclass correlations can be negative, yet they are a ratio of two variances -- the variance of the means of the classes to the variance of the entire set of values. What is a neat ...
0
votes
0answers
24 views
Iterative Computation of Correlation Coefficient
Given a set of $k$ data points $A$, I have the correlation coefficient between them as $\rho_A$. Now I want to iterate over a new set of data points $B$ (say $j$ of them) and wish to iteratively ...
0
votes
2answers
34 views
Correlation bound
Let x and y be two random variables such that:
Corr(x,y) = b, where Corr(x,y) represents correlation between x and y, b is a scalar number in range of [-1, 1]. Let y' be an estimation of y. An ...
0
votes
0answers
30 views
how to compare correlation between random variables?
Suppose I have a random variable, S(k) for starting date of callable bonds, M(k) for the maturity date of the bonds, and C(k) for the called date of the bonds.
$$S(k) < C(k) < M(k)$$
C(k) is ...
3
votes
1answer
160 views
quadratic relationship
Detection of linear relationship is possible with correlation coefficient. If absolute value of correlation coefficient is 1, then the relationship is linear.
Is there any way for detecting quadratic ...
0
votes
1answer
44 views
Relationship between Correlation and Bayes Theorem
Is there some relationship between the correlation of two random variables, and Bayes Theorem?
A bit of background intuition,
if W = random variable denoting number of women in a room, and L = ...
1
vote
0answers
19 views
Estimating the likelihood of independence of two discrete variables using the co-occurrence count matrix.
I have some data about users from different regions visiting different directories of some website. Aggregating that data I get the co-occurrence frequency matrix (for regions and directories). Now I ...
1
vote
0answers
58 views
Pearson correlation and metric properties
Assuming that the data set was $z$-standardized to zero mean and unit variance (also assuming that it does not contain constant vectors).
Then Pearson's r reduces to Covariance:
$$\rho(X,Y) := ...
0
votes
0answers
34 views
Correlation Coefficient dealing with discretely distributed variables
I'm a bit stuck on this practice problem I have for my HS business stats class. I'd appreciate any help to get the solutions. Thank you.
Exercise #22: Let X and Y be discretely distributed random ...
1
vote
3answers
604 views
Correlation between three variables question
I was asked this question regarding correlation recently, and although it seems intuitive, I still haven't worked out the answer satisfactorily. I hope you can help me out with this seemingly simple ...
1
vote
0answers
83 views
Cross-Correlation (and finding Correlation error ) of two digital sequences.
In a IEEE paper, I saw a formula for WUInt(ti+1) as , Reference :
...
2
votes
1answer
31 views
Find data to perform regression analysis
I'm trying to find some data (two continuous variables that I believe are correlated) online for which I can perform a regression anaylsis, my assignment sheet says:
The data may be found anywhere ...
1
vote
0answers
61 views
Compute significance of Kendall tau-b?
I have so-far tried all ways of computing kendall tau significance (where there are ties) described here.
However, none of them works good, even for relatively large vectors. I think the problem is ...
