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

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2
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0answers
1k 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
164 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
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1answer
20 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 ...
1
vote
1answer
192 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
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1answer
154 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
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2answers
108 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
1answer
216 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
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1answer
84 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
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2answers
2k 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 ...
1
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2answers
135 views

Does $0$ correlation imply independence for marginally normal distributions?

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
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0answers
51 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
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1answer
136 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
221 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
119 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
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1answer
295 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
2answers
65 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 ...
3
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1answer
1k 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
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1answer
203 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
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0answers
23 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 ...
2
votes
1answer
538 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) := ...
3
votes
4answers
8k 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
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0answers
232 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
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1answer
130 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
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0answers
95 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 ...
3
votes
1answer
164 views

Autocorrelation of wrapped Wiener process

Let $\phi(t)$ be a Brownian Walk (Wiener Process), where $\phi\in[0,2\pi)$. As such we work with the variable $z(t)=e^{i\phi(t)}$. I would like to calculate $$E(z(t)z(t+\tau)).$$ This is equal to ...
2
votes
2answers
667 views

Time series and social network analysis

I am interested about plotting graphs of a phenomenon and study it using tools from social network analysis. Suppose the nodes are time series, and that the links between the nodes are the correlation ...
0
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0answers
235 views

Autocorrelation derivation using fourier transform

I am stuck with basic understanding of the Auto-correlation derivation of a simple signal and I would be pleased if you could help me out with that. Lets have a signal $x(t)=\cos(2\pi{f_{0}}{t})$. ...
2
votes
2answers
309 views

Relationship between variances in perfect correlation

I have two random variables $X$ and $Y$ with mean and standard deviation $(\mu_1,\sigma_1)$ and $(\mu_2,\sigma_2)$ respectively. I know that for perfect correlation the relationship is given by a ...
1
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1answer
293 views

Find correlation of x and y, given E(Y|X) and E(X|Y)

Suppose that X and Y are random variables such that E(Y | X) = 7 - (1/4)x and E(X | Y) = 10 - Y . Determine the correlation of X and Y . Edit: So far I've got E(x)=4 E(y)=6 Now I'm trying to ...
1
vote
1answer
200 views

How to increase the correlation?

I have three vectors of numbers with the same dimensionality, $A$,$B$ and $C$. What is the most suitable number $x$, which maximizes the correlation of $A$ and $B+xC$ . To what extend can I increase ...
1
vote
1answer
62 views

How can I show that $z_i =\cos(iw)$ where $w$ is uniform on $[0,2\pi]$ is a white noise process?

How can I show that $z_i =\cos(iw)$, where $w$ is uniform on $[0,2\pi]$ is a white noise process? So far, I have shown $E(z_i)=0$ by integrating. However, I need to show ...
0
votes
2answers
801 views

Step by step correlation calculation

I must understand how I can calculate the correlation for the following probability variables. ...
1
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2answers
278 views

Linear vs non-linear Correlation

How do i check that two random variables satisfy the requirements for computing correlation via Pearson or Spearman? If the data is non-linear/ non-Monotonic, are there other tests i could use to ...
5
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1answer
161 views
+100

Correlation between an event and a time series

I have a time series, e.g. the daily number of visitors on my blog. I have a set of events of some class, like the days when I made a new posting. I want to measure the effect of a new posting on the ...
1
vote
3answers
1k views

Determinant of a N symmetric square matrix with diagonal 1

What is the determinant of a symmetric $n \times n$ matrix with all diagonals be 1 and all others are $\rho$ (yes correlation matrix)? Anyone can tell me a method to work it out elegantly? Thanks!
5
votes
2answers
842 views

Eigenvalue decomposition of block covariance matrix for Canonical Correlation Analysis (CCA)

Edited: My question is related to a tutorial I was reading. The covariance matrix is a block matrix where $C_{xx}$ and $C_{yy}$ are within-set covariance matrices and $C_{xy} = C_{yx}^T$ are ...
1
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1answer
152 views

Independence of quadratic forms

Let us consider the quadratic form $$q_1 = \mathbf{x}_1^\mathrm{H} \mathbf{A}\,\mathbf{x}_1 $$ and the quadratic form $$ q_2= \mathbf{x}_2^\mathrm{H} \mathbf{A}\, \mathbf{x}_2 $$ where ...
0
votes
3answers
251 views

Prove dot product will get maximum

If we have two identical sets $A_1 = A_2 $, and we were asked to get the maximum sum of multiplying one distinct element from $A_1$ by another distinct element of $A_2$, for all elements in $A_1$. ...
2
votes
0answers
246 views

Correlated diffusion processes and covariance matrix

I'm really noob in maths topics so I hope you will excuse me if I use terms which aren't correct. I would like to simulate $n$ dimensional diffusion processes with $n$ noises. Each process has its ...
3
votes
2answers
305 views

Correlation and squared variables

According to my textbooks if two variables are uncorrelated, they are not necessarily independent (unless they are normally distributed). My question is, are 2 variables still not independent if they ...
4
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1answer
72 views

PCA vs Correlation

What is the relationship between (first) principal component(s) and the correlation matrix or the average correlation of the data. For example, in an empirical application I observe that the average ...
0
votes
1answer
318 views

Difference between positively correlated graph and a linear relationship?

So I understand the differences between positive and negative correlation and so on. However what I don't understand are the similarities and differences between a positive correlation and a linear ...
2
votes
3answers
146 views

Product of standard deviations

If $u=cx+dy$ and $v=cx-dy$ and $R$ is the co-efficient of correlation between variables $x$ and $y$ and variables $u$ and $v$ have 0 correlation, then how can I prove that ...
2
votes
1answer
745 views

Calculate a whitening matrix without using inverses?

Consider a random column vector $\mathbf{x}$, of dimension $m$. That is, it is a random vector, composed of $m$ random variables. The PDF of the random vector $\mathbf{x}$ is thus the joint-PDF of its ...
2
votes
1answer
100 views

Nonlinear regression with correlated errors

it's my first post here and I'm a newbie in statistics, so please forgive me if I'm doing something wrong or explaining myself badly. Anyway, I have a problem similar to this: How to perform ...
3
votes
0answers
163 views

How to perform nonlinear regression with correlated errors?

I have a nonlinear least squares problem, but the errors are correlated. I could use R's nls function to do the regression if the errors were independent, but I don't know the right way to handle ...
1
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0answers
122 views

Windowed Linear Correlation

$\DeclareMathOperator \Cov {Cov}$ $\DeclareMathOperator \Var {Var}$ $\DeclareMathOperator \E {E}$ Consider the following experiment: For $N\geq1$, consider $N$ black balls. Let us paint each black ...
3
votes
1answer
652 views

Necessary and sufficient conditions for a matrix to be a valid correlation matrix.

It's not too hard to see that any correlation matrix must have certain properties, such as all entries in the range -1 to 1, symmetric, positive semi-definite (excluding pathological cases like ...
4
votes
2answers
148 views

Correlation in errors

I'm not good in statistics, so please excuse my noob question. We want to ask a question from people (say what is $2+2$). They might make mistake. We assume that they give the correct answer with the ...
1
vote
1answer
330 views

Pearson Product Moment Correlation Coefficient for linear relationship only?

Pearson Product Moment Correlation Coefficient method is used only if variables are linearly correlated. But if they are linearly correlated, then correlation coefficient $$r=\pm 1$$ only. Then why we ...