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

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40 views

Is there any measure for detecting quadratic or cubic relationships?

Correlation coefficients is a useful measure for detecting linear relationships. Is there any measure for detecting linear relationship between one dependent variable and more than one independent ...
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62 views

Correlation function of an asymptotically stationary AR process

I have a great confusion with the autocorrelation function of an AR process. Its derivation usually follows in this way (Haykin, 2007): The difference equation for an AR(M) process, $u(n)$, is ...
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1answer
23 views

Correlation coefficient and orthogonality

In the book Matrix Analysis and Applied Linear Algebra, the author describes the coefficient of linear correlation as $$\frac{(x-\mu_xe)^T(y-\mu_ye)}{||x-\mu_xe||\cdot||y-\mu_ye||}$$ where $x,y\in ...
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1answer
100 views

Linear correlation in 3D?

What's the name of a statistical method used to determine the goodness of fit of a series of points in 3D space that are to be fitted on a regression line ? I can calculate a regression line and the ...
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0answers
23 views

Generating random variables with specific higher order correlations

I would like to generate a series of random variables {$X_1,X_2,...$} with the following properties: 1) $\langle X_i\rangle=1$ for all i. 2) $\langle X_i \cdot X_j \cdot X_k \cdot ...\rangle=0$ ...
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2answers
25 views

Identifying modules in a correlation matrix

I am a biologist with some maths background... but not enough knowledge to solve this problem, so I would be really grateful if someone could help (and explain it at a level that a biologist might ...
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0answers
14 views

Autocorrelation of a signal known only on an interval of finite size

Let's consider we have a continuous random signal ${ t \in ] - \infty \,;\, + \infty [ \mapsto b (t)}$. We assume this signal to be stationary, so that when ensemble-averaged, one may introduce the ...
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44 views

Limit of Covariance and Correlation of Random Walk

Let $S_n=X_1+...+X_n$, $n\geq1$ be a random walk, where $EX_k=\mu$ and $Var(X_k)=\sigma^2$, $0<\sigma^2<\infty$. a)Find the covariance $Cov(S_n,S_m)$ and the correlation coefficient ...
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1answer
50 views

Is there a simpler way to calculate correlation?

Let's consider that a variable y constructed from x $x_i ∈ \left\{1,3,5,7,8\right\}$ $f(x_i)=2x_i+1$ $y_i=f(x_i) + ε_i, ∀i∈ \left\{1;...;5\right\} $ where $ε_i$ is a ...
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0answers
21 views

Variance of estimating coefficients by correlating a sequence

I have a sequence $$ r[n] = a_1.t_1[n] + a_2.t_2[n] + a_3.t_3[n] + ... $$ where $t_1, t_2, t_3,...$ are uncorrelated, two-level (+A/-A), zero mean, pseudo-random sequences. To estimate $a_1$, ...
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18 views

Why are the Real and Imaginary parts of a field in k-space uncorrelated?

I am in the process of generating a (real) Gaussian random field $\delta(\vec{x})$ from a given power spectrum $P(k)$. The way I define the power spectrum is, in Fourier space, $\left\langle ...
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22 views

Properties between Pearson correlation of two function and the correlations of their derivatives

For two functions, $f(t)$ and $g(t)$, I can calculate the Pearson correlation $Corr$. Does the correlation, $CorrD$, between the derivative functions, $f'(t)$ and $g'(t)$, has some properties with ...
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1answer
129 views

The relationship between diagonal entries and eigenvalues of a diagonalizable matrix

Let $\mathbf{C}$ be an $n\times n$ Hermitian matrix. Let $\dagger$ indicate a matrix conjugate-transpose. Let $\mathbf{V}\mathbf{D}\mathbf{V}^\dagger$ be the eigendecomposition of $\mathbf{C}$, where ...
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0answers
32 views

similarity between two ranked sequence

How can I measure similarity/distance between two sequences of ranked numbers/letters. The two sequences are of different length, and only have some elements in common? For example, if I have three ...
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0answers
25 views

Concentration bounds on Pearson correlation matrix

I am interested in (rather sharp if not the finest) tail/concentration bounds for the Pearson correlation matrix: let $X_1,\ldots,X_N \sim \mathcal{N}(0,1)$ be correlated random variables; let ...
0
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1answer
61 views

If $X$ and $Y$ are Normally distributed with correlation $\rho$, can we say anything about $E[Y \mid X]?$

Let $X \sim N(0, 1)$ and $Y \sim N(0, 1)$ and $\mathbb E[XY]=\rho$. Can one say anything about the conditional expectation $\mathbb E[X \mid Y]$? In general, this clearly does not seem to work, ...
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1answer
29 views

inference of causality for binary variables

Let's say that a data set has N random binary variables Xi and we want to infer which of these variables have a causal relationship with X1. The following table would describe the data, where each ...
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1answer
99 views

How should I calculate a rolling autocorrelation?

I have an array of data $ \mathbf{y} \in \mathbb{R}^n $, and I need to calculate the lag-1 autocorrelation between sections of this array 7 elements long. For all intents and purposes, we can imagine ...
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1answer
42 views

Do 'X' and "y' have 'zero' correlation , or can be anything between '-1' and '+1'?

let , we have bi-variate data on X and Y . Now corresponding to the value $x_0$ , y can take any value.but for all other values of x , y takes a constant value. what will be the correlation ...
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0answers
39 views

Non-orthogonal space

What does the angle between two non-orthogonal basis denote? Is it correlation or some measure of dependence. Does that mean that coordinates of a point if moved in the direction of one axis also ...
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0answers
45 views

The concept of correlation in functional analysis

I am currently reading a book "measure, integral and probability" by Capinski and Kopp. The correlation between random variables $X$ and $Y$ is defined as the cosine of the angle between $X_c$ and ...
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2answers
50 views

Pearson's R and Correlation formula

I'm trying to make sense out of Pearson's $R$ and Pearson's correlation coefficient. I'm not sure I really see a difference. Let me just clear out any confusion, for me Pearson's $R$ is: $$ R = ...
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1answer
26 views

Interpretation of $N$ and $p$ in Pearson’s correlation test?

In this paper, the authors report an estimate of $r = 0.86,\, N = 28,\, p < 0.001,$ using Pearson’s correlation test. The parameter $r$ (or $\rho$) is clear to me, but how are $N$ and $p$ derived ...
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53 views

Determining statistical correlation between XYZ points

I have a set of two 3D points, both 3D points (two points in each set) representing the same object - just in different states (State A, State B). I'd like to see if it's possible to predict the ...
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0answers
50 views

partical correlation in mixed case binomial and gaussian

For Gaussian mutlivariate distributions it is known, that zero partial correlation corresponds to conditional independence. Is there a same result if one of the variables has a binomial distribution? ...
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1answer
107 views

sufficient conditions for a stochastic process to be wide sense stationary

From the page Stationary process, I have the following definition: WSS random processes only require that 1st moment and autocovariance do not vary with respect to time and from the page ...
3
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1answer
118 views

Covariance of 1-D random process is $n\times n$!!!!

I'm reading a tutorial on stochastic processes. There is an example in the tutorial as follows: General Moving Average random process given as $X[n]=\frac{(U[n]+U[n-1])}{2}$ where $E[U[n]]=\mu$ ...
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0answers
25 views

DFT of subdomain of periodic domain

$f(t_i,x_j)$ is a solution of stochastic differential equation on grid. $j=[0,N+1]$, $i=[0,\infty]$ and boundary conditions are periodic: $f(t_i,x_0) = f(t_i,x_N)$ and $f(t_i,x_{N+1}) = f(t_i,x_1)$ ...
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0answers
41 views

Multiple variable correlation

I have three data variables (let's call them $A$,$B$, and $C$) that each consist of $14$ samples. What I know is that the combination of $A$ and $B$ is related to $C$. I don't know what kind of ...
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1answer
52 views

does uncorrelation extend to product of complex random variables?

Give two uncorrelated complex variables, $X$ and $Y$. Are $XX^{*}$ and $YY^{*}$ also uncorrelated, where $*$ means complex conjugation?
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15 views

combining correlation from two different time periods

Suppose I have two time-series $X_t$ and $Y_t$ and I measure their correlations over two different time-periods $\rho_1 = corr(X_i, Y_i)$ for $i \in (t_{1a}, t_{1b})$ $\rho_2 = corr(X_i, Y_i)$ for ...
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2answers
50 views

Finding Linear independent vectors

Thanks for clarifications. Now i am posting the question in a different way. Suppose a vector $V$ is orthogonal to vectors $X1$ and $X2$. $X1$ and $X2$ are linearly independent. Now if $V$ is also ...
0
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1answer
19 views

In a simple regression model estimated using OLS, the covariance between the estimated errors and regressors is zero by construction

Is this statement true or false? I seem to remember that this relationship does not hold when the regression has no intercept, however my teacher said that this was true regardless of whether we ...
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1answer
12 views

How represent correlation of $(f_i - f_j) $ and some $ y$ by $cov(f_i, f_j)$, $cov(f_i, y)$ and $cov(f_j, y)$?

I am reading this paper: Face Alignment by Explicit Shape Regression. One of the significant step of algorithm which proposed in these paper connected with correlation. But my knowledge about ...
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1answer
44 views

Correlation coefficients of X and Y [closed]

I was wandering if anybody could help me with the following question. I am fairly new to correlation coefficients and was attempting to tackle this question but was unsure how to do so? Thanks.
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2answers
194 views

Generating correlated random variables with discrete distribution

I would like to find a simple way to generate two correlated random variables under the condition that each r.v has a same discrete distribution (for example Bernoulli distribution) This link provides ...
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2answers
41 views

Calculating the correlation coefficient between least square estimates

PROBLEM STATEMENT: Consider the following 2-variable linear regression where the error $e_i$ 's are independently and identically distributed with mean $0$ and variance $1$; $$y_i = α + β(x_i − \bar ...
0
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1answer
36 views

Cross-correlation of identical sets: not getting expected result

I'm trying to work out the correlation coefficient of two sets using a given formula, but I'm not getting a perfect correlation when using identical sets. The correlation between a client’s ...
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0answers
29 views

Transpose is just the way of generalizing a dot product?

It seems like $a^Tb$ is the same as writing $a \cdot b$ in matrix form. 1) Why is $n \times 1$ and $n \times 1$ matrix multiplication undefined? 2) Is this just a generalization of the dot ...
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0answers
20 views

How to find covariance matrix from correlation if mean is not given?

I'm given autocorrelation function of gaussian random process: $$ R_x(\tau) = 3e^{|-\tau/3|} $$ Now I should find covariance matrix. I know the formula and solutions, where $$ C_{xx} = R - E[X]E[Y] $$ ...
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1answer
30 views

Question about uncorrelatedness of random variables and distributions

I was wondering, if two random variables are dependent, does that mean that they must be correlated? does one imply on the other or vice versa? Also, if I know that a joint distribution of two ...
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0answers
36 views

Generalizing Pearson's coefficient to determine properties of embedded manifold

I have the following dilemma: We know that for random vectors we have Pearson's coefficient of skewness. I think you all agree that in some sense it measures the shape properties of the ...
0
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1answer
33 views

correlation matrix of an AR(1) process

Suppose we have a process whose elements follow an AR(1) pattern with correlation $\rho$. I am confused, concerning the following: The exact form of the $(i,j)$ element of the correlation matrix P is ...
0
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1answer
232 views

How can I remove correlated noise spikes from 2 signals?

I have some MRI data collected across time. When the patient moves, this results in a spike in the signal (so I guess it's not really "noise"). I would like to identify and remove these. So far I ...
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1answer
37 views

Ratio laying within the confidence interval still being depicted as having an influence?

I keep seeing this in research papers. The researchers claim that there is a positive correlation between A and B then subsequently show that they odds ratio/sample mean etc. is IN the confidence ...
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2answers
1k views

Question on Spearman's Rank Correlation Coefficient

I'm doing some practice questions in my statistics book, and started doing this one: Find Spearman's rank correlation coefficient between X and Y for this set of data: ...
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0answers
57 views

Calculate mean and correlation of a stochastic process

I am given the Stochastic process $Y_n$, where $n \in Z$ defined by: $ Y_n = X_n - X_{n-1}$ where $X_n$ is a process with independent and identically distributed geometric variables $X_n \sim G(p)$ ...
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0answers
20 views

Correlation between ordinal variables

I want to know the correlations between 3 groups of variables which are oridinal (rating of 1 to 10). I have followed the formula on wiki and computed the Kendall tau-b correlation coefficients ...
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0answers
48 views

Limit of correlation function using transfer-matrix method

This question is about a stochastic process theory. I really very bad in this topic. That's why I have to ask for help. I may mistranslate some terms but I'll do my best to give you right information. ...