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

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9 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
5 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 ...
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1answer
39 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
18 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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0answers
11 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
36 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
23 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 ...
2
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0answers
30 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
15 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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0answers
9 views

Good broad review of agent-based modeling? [on hold]

Trying to find some good review of agent-based models and networks, covering what is called "opinion dynamics", correlated behavior of agents, phase transition analogies, etc. Are there any articles ...
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1answer
20 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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13 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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32 views

How to rotate two 2D ellipses such that they have maximum cross corelation?

Suppose I have two matrices $A=\begin{pmatrix}3 & 1 \\ 1 & 4\end{pmatrix}$ and $B=\begin{pmatrix}5 &-2 \\ -2 & 4\end{pmatrix}$, where $A$ and $B$ represent covariance ellipses in 2D. ...
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0answers
41 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
39 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
67 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
18 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
14 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
38 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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0answers
4 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
44 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 ...
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1answer
10 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
7 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
39 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
61 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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0answers
9 views

Autocorrelation of a random sequence is given below. A way to shuffle to decorrelate?

3.0000 1.7071 - 1.7071i 0 - 1.0000i 0.2929 + 0.2929i 1.0000 0.2929 - 0.2929i 0 + 1.0000i 1.7071 + 1.7071i The ...
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2answers
29 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 ...
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1answer
33 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
23 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
14 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
22 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
35 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 ...
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1answer
24 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
61 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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2answers
34 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
38 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
17 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
8 views

What are the bounds on total correlation given partial correlations?

Given two random variables X and Y, each with 3 million outcomes, if we compare the first, second, or third million of these outcomes, we can compute the partial correlations between X and Y. If each ...
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0answers
28 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. ...
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0answers
59 views

Minimize correlation between input and output of a linear system

I am not sure if "minimize correlation" is the right title for this issue but I could not find a better sentence to describe what I would like to achieve. Let's say that I have a black box with ...
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1answer
39 views

Why is my phase correlation not equal to the real correlation?

If I understand the correlation theorem correctly, it states: $ f(x,y) \unicode{x2606} \bar g(x,y) = \mathfrak{F}^{-1} \left\{ F^*(u,v) G(u,v) \right\}, $ also called a phase correlation. Above ...
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1answer
16 views

Does correlation (PMCC) require variables to be normal

When calculating product moment correlation coefficient between two variables, say height and weight, is it necessary that the variables are normally distributed for the PMCC to be valid/relevant. ...
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1answer
19 views

Statistics for correlations with many (0,0) values

Suppose you have a large but finite collection of tweets. You want to know whether talking about football tends to correlate with talking about basketball. You can generate a table for a few hundred ...
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0answers
12 views

Question about the relationship between correlations

I am trying to figure out the relationship between correlations of variables where one of the variables defined as the difference between two other variables. I have variables x and z, which are ...
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1answer
26 views

Finding peaks and oscillations in a signal

I am working on a problem where I'm analysing a signal and trying to find a measure of whether a roughly Gaussian shape appears or oscillations - though the oscillations may not be periodic. For ...
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1answer
30 views

Law of large numbers with correlated variables

My sample is a series of measurements of the variable $x$. Measurement t, $x_{t}$, is correlated with $x_{t-n}$. However, as n tends to infinite the correlation tends to zero. If the sample grows, ...
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2answers
38 views

Correlation in scatter plot

This may be a very basic matter for statisticians, but I still have no intuition for this sort of thing. Here goes: I have two quantities (the nature of which is irrelevant) which I suspect to be ...
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0answers
31 views

explanation : Example of Gaussian random process?

Can any one explain to me how to answer the question and what is the Gaussian random process in a simple way. I know how we find the C xx from R xx the rest of the answer I don't understand why all ...
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0answers
23 views

Correlation/Regression for Continuous and Discrete data

I want to correlate a data where one axis is continuous (ranging from 0 to 1), other axis is discrete. Discrete axis scale is 1 to 5 (1 is for Strongly Disagree and 5 is for Strongly agree). How ...
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0answers
32 views

Calculation the Correlation Matrix of a Random Observation Vector

I've googled and looked around on StackExchange but I can't quite find the answer. I'm trying to calculate the correlation matrix R. Below I've included a screenshot of some text that explains how. ...