For questions about correlation of two random variables. Use it with [tag: random-variables] and [tag: probability].

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1answer
38 views

correlation estimator variance

Consider I have realisations of two random variables $X$ and $Y$ and I estimate their correlation thanks to the classic formula : ...
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1answer
26 views

correlation matching audio files peak position

if i cross correlate an audio file with itself (which means there is no delay or difference), the peak position should be a zero or at the center of the cross correlation? that is really confusing ...
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1answer
33 views

Convolution module

I am trying to apply GCC-PHAT algorithm here to process audio files and find delay between them. Im coding using Android and Java with the help of this library, and comparing the results with Matlab. ...
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0answers
82 views

Expectation and convolution question.

I am learning in an image processing course, and the professor did the following: As part of a derivation, has this: What I do not understand, is how he was able to remove $r(i,j)$ to the ...
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1answer
63 views

Correlation coefficient of i.i.d variables

Let $X_1, X_2, X_3, ...$ be i.i.d variables, and for every $i$ $X_i$ has variance. Define $S_k=\sum_{i=1}^{k}X_i$. Calculate $\rho(S_m,S_n)$ for $m\leq n$. Well, I know it should be $\sqrt{ m/n }$, ...
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17 views

factor analysis for given data

suppose that we have following data i have done covariance matrix and eigenvalue decomposition ...
1
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2answers
36 views

Finding the correlation coefficient of ordered statistics

I am working on the following problem. Let $$X_{(1)}, \ldots ,X_{(n)}$$ be the order statistics from the uniform distribution of $[0,1]$. Find the coefficient correlation of $X_{(1)}$ and ...
1
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1answer
45 views

How do you prove that if $ X_t \sim^{iid} (0,1) $, then $ E(X_t^{2}X_{t-j}^{2}) = E(X_t^{2})E(X_{t-j}^{2})$?

Suppose we have a time series $X_t$ s.t. $X_t \sim^{iid} (0,1)$. How do you prove that if $ X_t \sim^{iid} (0,1) $, then $ E(X_t^{2}X_{t-j}^{2}) = E(X_t^{2})E(X_{t-j}^{2})$? Or, I guess, if ...
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53 views

Correlation coefficient calculation

Why do we remove of the mean of the data while calculating the correlation coefficient value of bivariate data in statistics? DotProduct/ProductOfLengthOfVectors should always give anyway a ...
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0answers
31 views

Multiple correlation

My question is very elementary. I need to implement a software that computes the multiple correlation of a set of datas that I have. In order to do that, I need would like to find the generic formula ...
0
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1answer
35 views

How can you compare two mathematical functions of single variable? [closed]

I have some functions and want to see how close one function is to the other. One way to check is correlation. What are the other ways of checking the "similarness", "closeness" or "nearness"?
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2answers
38 views

What is this idea of “Minimum Correlation”?

So I was having a read of this paper here: Minimum correlation for any bivariate Geometric distribution. On the first page of he paper we encounter the following definition of "minimum correlation": ...
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1answer
25 views

Mutual information decrease with coarse-graining

Let $X,A,Y,B,C,D$ be random binary variables. $D$ is independent from $X,A,C$ and $C$ is independent from $Y,B,D$. Is it true that: If $I(Y:B|D=0)\leq \epsilon$ then $I(X\oplus Y:A\oplus ...
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2answers
48 views

Autocorrelation and var-cov matrix

$$Y_t=\beta_1+\beta_2 X_{t2}+\dots +\beta_k X_{tk}+\epsilon_t \qquad (t=1,\dots,T)$$ $$\epsilon_t=\rho \epsilon_{t-1}+v_t, \qquad v_t \sim \mathrm{i.i.d.}(0,\sigma^2_v)$$ GLS estimation under AR(1) ...
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2answers
33 views

Determine range of $\rho$ in correlation matrix

I was asked a question and I was wondering if you can help solve it. Given are $3$ random variables $A$, $B$and $C$ all having the same correlation. So the correlation matrix looks like: ...
0
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1answer
23 views

Does correlation have to be in the context of (Gaussian) normal distribution?

I am not quite familiar with the concept of correlation. The Pearson's correlation coefficient is defined as: $\rho_{X,Y}=\mathrm{corr}(X,Y)={\mathrm{cov}(X,Y) \over \sigma_X \sigma_Y} ...
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1answer
49 views

How to calculate the HHG (Heller Heller Gorfine) correlation

HHG (A consistent multivariate test of association based on ranks of distances) is introduced in: Heller, R., Heller, Y., & Gorfine, M. (2012b). A consistent multivariate test of association ...
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1answer
58 views

Correlation with many zero values

I have data for selling books from 2 bookstores for 100 days. For the first 90 days, no book was sold. Then the following books were sold Day# - BookStore1 - BookStore2 Day1 - 0 - 0 ...
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2answers
51 views

Strong vs weak relationship in this correlation

I produced this plot and regression line in R and I thought my results were quite odd. Is the relationship of the correlation determined by how steep the regression line is? So in this case it isn't ...
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1answer
76 views

Variance from joint random variables?

So I have 20 different 'weeks' that are being considered as part of a weight loss exercise. The weight lost each week is distributed normally around mean $\mu =0.8kg$ and std. deviation $\sigma^2= ...
1
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1answer
309 views

How to explain tie-correction for Spearman's Rank Correlation?

In Mathematics at my college we are being taught correlation in which when there are ties in ranks we take average rank for all of the ties and then total correction factor is added summation of ...
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1answer
111 views

graph in excel to represent correlation of 3 parameters

I have some data in excel and I would like to make a graphical representation of those data. Structure of my data: persons ID : from 1 to 485 to every person, there is one parameter like average ...
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1answer
69 views

Correlation between two random variables

Show that if $\rho_{XY} = +1$ then $X=a+bY$ for some constants $a,b$ and $b>0$. How would I go about showing this? Note: $$ \rho_{XY} = \frac{\mbox{Cov}(X,Y)}{\sqrt{\mbox{Var}(X)\mbox{Var}(Y)}} ...
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1answer
50 views

Correct way to evaluate correlation of a computer model with multiple human annotator scores

I have posted this question to CrossValidated without lack. If anyone from this community can give some insights, I would be really grateful. Assume we have 3 annotators, each one of which has ...
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2answers
32 views

Showing $Cor(X,Y) = 1$ if $a>0$ and $-1$ if $a<0$

Suppose X and Y are random variables such that $Y=aX+b$ and $a$ and $b$ are constants. Show that $Cor(X,Y) = \begin{cases} +1 &\mbox{if } a > 0 \\ -1 & \mbox{if } a < 0. \end{cases}$ ...
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1answer
24 views

Comparing ranking algorithms

If I have several different ranking algorithms and a 'correct' ranking, is there a good way of "scoring" the alternative rankings given by the algorithms against the reference one? For example: ...
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1answer
41 views

Linear regression with normalized variables

Suppose I have two variables X and Y such that mean(X) = 0 = mean(Y) and sd(X) = 1 = sd(Y). The slope of the linear regression line for Y vs X is cov(X,Y)/var(X) = corr(X,Y) since X and Y are ...
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0answers
79 views

Autocorrelation Function and Power spectrum from ACF

In my assignment I am required to write or use a C code to find the autocorrelation function of a given function and then find the power spectrum from it. The function is as follows: $$f(t) = \cos(10 ...
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0answers
25 views

correlation estimator

Suppose I have independent variables $X$ and $Y$ which follows exponential distribution with parameter $\lambda$. I want to find the variance of correlation estimator $\hat{\rho}$ which is defined as: ...
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0answers
17 views

stats project - good model, what to do with it?

I've recently been working on a stats project for school. I have been comparing a country's 'quality of life index' with 'moral' opinions survey to see if there are relations. Here's some example ...
0
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1answer
24 views

correlation between two series

let us consider following two series $$y[t]=a_1\sin(\omega_1 t + \phi_1) + a_2\sin(\omega_2 t + \phi_2)+ \cdots + a_p\sin(\omega_p t+\phi_p) + z_1(t)$$ and $$y_1 [t] = A_1(\sin(\omega_1 t+\phi_1) ...
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0answers
15 views

Maximum correlation of n variables

For $n>2$ variables, one cannot arbitrarily choose the correlations $\rho_{ij}$ because the resultant correlations must obey the law of cosines. Equivalently, the covariance matrix between them ...
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2answers
47 views

Variance of X - Y

If X and Y are random variables with correlation coefficient 0.7, each of which has variance 6, what is the variance of X−Y? Enter your answer as a decimal. Using the information given, I was able ...
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2answers
39 views

Covariance of $10$ Coin Flips

I'm getting the hang of using the properties of Covariance to make calculating it much easier but I'm stuck on this one. Fair coin tossed $10$ times. Let $X$ denote number of heads observed and ...
1
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2answers
75 views

Covariance of three dice rolls

I understand this question has been asked but I have a different comment to make on the matter and wondering if someone could help me. Let Z1,Z2,Z3 be values resulting from three tosses. ...
1
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1answer
32 views

Simple linear regression prove variables are uncorrelated:

I am working on the following problem: In a problem of simple linear regression, $$Y = \hat\beta_0 + \hat\beta_1 x(bar),$$ show that the random variables $\hat\beta_1$ and $Y$ are un-correlated (All ...
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1answer
60 views

Fair Coin Covariance

Consider an experiment in which three fair dice are tossed simultaneously and independently. Let $Z_1,Z_2,Z_3$ be the values resulting from the three tosses. Define $X=Z_{21}+Z_{22}−Z_{33}$ and ...
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1answer
25 views

What does the “empirical” autocovariance function represent?

My professor gave me the sequence ${X_n} = {1,5,5,1,5,5,...}$ and asked us to compute the empirical autocovariance function given below. $$\displaystyle \hat \rho(1) = \lim_{N \to \infty} \frac{1}{N} ...
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2answers
39 views

Is the autocovariance function of a sequence identically zero if the sequence is iid?

My professor gives the following definition for the autocovariance function. $$\rho(i,j) = Cov(X_i , X_j)$$$\\$If I have a sequence that is iid, when i compute $\rho(n,n+1)$ for $n \geq 0$, I found ...
2
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1answer
464 views

Distribution of the sum of normal random variables

Let $X\sim \mathcal N(\mu_X,\sigma_X^2),\ Y\sim \mathcal N(\mu_Y,\sigma_Y^2)$ two normal random variables and $a,b\in \mathbb R$. If $X,Y$ are independent, then $$aX+bY\sim \mathcal ...
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0answers
13 views

Correlation matrix of time series is same as correlation matrix of its difference

I computed the correlation matrix between the percent change in the price of 6 stocks. Then I differenced the stock percent change data as if it was a time series, and the correlation matrix is almost ...
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0answers
21 views

Detecting camera shake

I have a bunch of data captured from a worm tracker that consists of a B&W camera that stares down at a few dozen worms for an hour at a time. The tracker captures the outline of each worm ...
0
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1answer
219 views

Autocorrelation and spectral density in MATLAB

This question is threefold. We have an LTI system that is a first degree Butterworth LP filter with the power TF where fu = 110Hz and ...
0
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1answer
450 views

Autocorrelation and spectral density in MATLAB

This question is twofold. We have an LTI system that is a first degree Butterworth LP filter with the power TF where fu = 110Hz and ...
0
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1answer
16 views

Autocorrelation of a sequence of vectors

Let's say I have a sequence of 2-d vectors and I want to calculate autocorrelation of this sequence of vectors. If $V_i$ where i = 1:n is the list of vectors then acf as a function of time lag 't' is ...
2
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1answer
41 views

$\rho_\gamma(X)=\frac{1}{\gamma} \log \mathbb{E}[e^{-\gamma X}]$

$\rho_\gamma(X)=\frac{1}{\gamma} \log \mathbb{E}[e^{-\gamma X}]$ is a convex risk measure, but it fails the subadditivity property in order to be called coherent. A mapping ...
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0answers
24 views

Cross correlation computations

What are useful ways/formula for calculating sample cross correlations (i.e. correlation factors between individual components of two different random variables). Say I have two sample matrices, $X$ ...
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0answers
10 views

Finding correct values based on information from two arrays

Consider the following scenario: Say, one machine is sending out a beep signal every 10 seconds in a very noisy environment. I have two sensors which detects these beeps independently. Device A is ...
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0answers
125 views

Generate correlated random numbers precisely

Let's assume I want to generate k samples of n random numbers, that are correlated according to a given correlation matrix C (e.g. $n = 3$): ...
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1answer
38 views

Correlation: Concept to Formula

In digital signal processing, we calculate the correlation between two discrete signals by multiplying corresponding samples of the two signals and then adding the products. Where does this ...