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Questions tagged [independence]

Events (or random variables) are independent when information on some of them tells you nothing about the probability of occurrence (/ distribution) of the others. Please DO NOT use this tag for independent variable use [predictor] instead.

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Combined reliability for statistically independent tests/measurements

I'm perplexed by this statement in Wikipedia article, 'Consilience': "Statistically, if three different tests are each 90% reliable when they give a positive result, a positive result from all ...
Jon Bragdon's user avatar
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1 answer
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Pearson chi square and correlation

My data are ordinal Pearson chi squared test value is 4.664 And asymp sig is 0.97 so the data are independent However pearson's R =-0.309 And the approx sig=0.037 Can they be independent and ...
Simona ysf's user avatar
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How to prove this relation for Kendall's distribution function (or Kendall's measure)

Kendall Distribution Function (Nelsen, 2006, p. 163) Or Kendall Measure (Salvadori et al., 2007, p. 148) Or Kendall Function (Joe, 2014, pp. 419–422) is the cumulative distribution function (CDF) of ...
khoshmard's user avatar
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Non-independent explanatory variable in regression [closed]

I've been getting a refresher course on regression online, no teacher, and in basically every cases aside from Generalized Linear Mixed Model, the independence of explanatory variable is assumed (...
Yo Pomdpin's user avatar
1 vote
1 answer
39 views

Generating highly non-independent random samples

I'm testing performance of statistical tests in the face of non-independent data and I'd like to generate random data where I know the underlying statistical distribution. The easiest way to do it is ...
Hubert Kario's user avatar
2 votes
1 answer
47 views

Regression with dependent observations of only one individual

Last week, I received a task to plan an analysis that my team wishes to perform. My objective is to measure if one physician agrees with the outputs that a certain tool generates for a set of N ...
kKodorna's user avatar
1 vote
1 answer
36 views

Multivariable analysis for an ordinal dependent variable

I am investigating the factors associated with self-perception of oral health. My dependent variable is self-perception of oral health, which is an ordinal variable measured on a 5-point Likert scale. ...
Nisha's user avatar
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Deriving the log-likelihood function for ACD (Autoregressive Conditional Duration) models

I am trying to understand the procedure that is shown in this survey to obtain the log-likelihood function to estimate the parameters for an ACD model: PACURAR, Maria. Autoregressive conditional ...
Residual Claimant 's user avatar
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26 views

Statistical test for unequal sample sizes of repeated measures (non-parametric)

I'm looking to understand the differences between various sources (50) that evaluate an event based on 8 ordinal scales (varying from 2 to 4 values) associated with a discrete score between 0 and 10, ...
ron's user avatar
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12 votes
3 answers
961 views

What does it mean for observations to be uncorrelated and have constant variance?

I am learning about linear regression from the textbook Elements of Statistical Learning by Friedman, Tibshirani, and Hastie. In this section they suppose we have a set of training data $(x_1, y_1), \...
CBBAM's user avatar
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Declustering impact, stationarity and discretization

I have a seasonal time series, and I am considering declustering (before any other preprocessing steps) it using runs declustering. If I observe an extremal index of 1, can I claim that my data is i.i....
Thoms's user avatar
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2 votes
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With $X$ and $Y$ being two independent $\text{Bernoulli(1/3)}$ rvs, show whether $U = |Y-X|,~V = X+Y$ are independent or not

Let $X$ and $Y$ be two independent $\text{Bernoulli(1/3)}$ random variables. Define random variables $U$ and $V$ as $$U = |Y-X|, \hspace{5mm} V = X+Y$$ Are $U$ and $V$ independent? I am new to the ...
Samar's user avatar
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0 answers
49 views

What is dependency on sequential data?

We know that Whenever the points in the dataset are dependent on the other points in the dataset the data is said to be Sequential data. A common example of this is a Timeseries such as a weather data....
D. S.'s user avatar
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2 votes
1 answer
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In general, does $P(R|N)>P(R)$ implies $P(N|R)>P(N)$ ? Seems to be confirmed by Venn diagrams example but contradiction with Bayes' theorem

Let $R$ and $N$ be two dependent events, such that $P(R|N)>P(R)$. Does this implies that $P(N|R)>P(N)$? The odds are this is true (and equivalently $P(R|N)<P(R)$ implies $P(N|R)<P(N)$). I ...
niobium's user avatar
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1 answer
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Independence assumptions in correlations when all data comes from same individual

This feels like a silly question, but anyhow - do the independence assumptions in common correlation tests matter much if all the data comes from the same individual and I don't want to make any ...
Dingbat's user avatar
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2 votes
0 answers
29 views

A/B Test for CTR without user-level data

Suppose I want to show two different ads and compare which one generates more clicks. By design I know that each user will see one of two ads at random every time s/he visits an external page where ...
ssrg's user avatar
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0 answers
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Dependence in ARCH empirical residuals

Suppose $R_1, R_2, \dots, R_T$ are observed values of ARCH(1) process ($R_i = \sigma_i z_i$). I then estimate ARCH(1) parameters $\hat{\omega}, \hat{\alpha}$ and calculate empirical standardized ...
Grigori's user avatar
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0 answers
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Are observations of different plots of the same farmer independent for a chi-squared test?

I have a pretty basic question. I have a dataset that has surveyed say 1000 farmers and their demographic data, and also surveyed the agricultural practices they undertake on each of their plots. Only ...
cha116's user avatar
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3 votes
1 answer
138 views

Estimate Standard Errors Effortlessly [closed]

I have an unobserved variable $𝑧_𝑖$, and three observed estimates of it: $𝑤_𝑖, 𝑥_𝑖, 𝑦_𝑖$. The errors $𝑤_𝑖−𝑧_𝑖,𝑥_𝑖−𝑧_𝑖,𝑦_𝑖−𝑧_𝑖$ are zero mean, independent of each other and ...
ba yes's user avatar
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2 votes
1 answer
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Can a GLM Binomial regression on repeated measures be seen as a trustworthy alternative for a Survival Analysis?

I'm working on an actuarial project to estimate monthly probabilities that someone becomes disabled. We have data available in a wide format. For example, the following lines are part of the data: ...
user avatar
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1 answer
44 views

within- and between-subjects variance and independence of observations

I came across some statements saying that if the within-subjects and between-subjects standard deviations are similar, the observations can be considered independent even if repeated measures exist (e....
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Are the p-values obtained on the same sample using synthetic AA tests (Monte Carlo) independent values?

Let's say we have the following procedure. We take a fixed sample of size n and perform the procedure 1000 time: we divide (split) it equally into 2 groups; we calculate p value using the F function (...
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0 answers
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Violation of i.i.d assumption in time series modeling

In time series forecasting,let's say you have $x_1, x_2, x_3, \cdots, x_t$ and the goal is to predict the the value of $x_{t+1}$ given values at previous times $1,\cdots,t$. Let's assume that the ...
Quqnus's user avatar
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3 votes
1 answer
97 views

Convolution with a pathological distribution

Problem definition Consider the following random bivariate vector \begin{equation} \begin{aligned} y&=z+v \\ z&\sim p_z(z;c) \\ v&\sim p_v(v) \end{aligned} \end{equation} where $p_z$ ...
matteogost's user avatar
0 votes
1 answer
41 views

Likelihood function of paired conditional logistic regression

I found the information about the likelihood of conditional logistic regression for paired data is few. The Wiki gives this answer, but I think it is wrong because event Yi1 and Yi2 are dependent, ...
Tom Hsiung's user avatar
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1 answer
153 views

Dependence through an unknown parameter?

Consider an urn from which we sample with replacement. Let $\pi$ represent the proportion of the urn's balls that are black, with the remainder being white. From a frequentist perspective, each ...
Trisoloriansunscreen's user avatar
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0 answers
15 views

What statistical test to compare survival curves for dependent data?

I'm currently doing time to event analysis for a cohort of participants. Each participant completed two different diagnostic tests for the same virus, and they did these every day for a week. ...
Matt's user avatar
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Looking for terminology to describe a certain partial independence condition on conditional probability

I find myself in a position where for events $X,Y$ and $Z$, I might have $$ P(X|Y,Z) = P(X|Y)P(X|Z) $$ I don't know what to call this, and it's difficult to search for potential phrases, since all ...
David Roberts's user avatar
1 vote
0 answers
51 views

Applying deterministic operators on i.i.d. random variables from the same probability distribution - what is conserved?

I have a collection of i.i.d. random variables xi, sampled from the same (possibly unknown) probability distribution, say P. Now I apply a deterministic operator on these i.i.d. random variables, e.g.,...
Abdullah T.'s user avatar
0 votes
0 answers
52 views

Conditional likelihood, conditional independence and joint independence

Consider a sequence of data samples generated from $n$ independent random vectors $(X_1, Y_1), (X_2,Y_2), (X_3,Y_3) ...$ $$D = (x_1,y_1), (x_2,y_2), (x_3,y_3) ...$$ Where $(X_i, Y_i)$ - is a random ...
spie227's user avatar
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1 vote
0 answers
28 views

What are the convincing examples of copulas uncovering not obvious statistical dependences (or the lack of them)?

What may be a good, strong and convincing example demonstrating the power of copulas by uncovering some not obvious statistical dependencies? I am especially interested in the example contrasting ...
AL1117's user avatar
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0 votes
1 answer
30 views

Conditional Independence: Equivalent Conditions

Let $X_1$ and $X_2$ be random variables, and $R(X_1)$ be a function of $X_1$. Here are two statements: (a) $X_1\perp\!\!\!\!\perp (X_2, Y) \mid R(X_1) $ (b) $X_1\perp\!\!\!\!\perp Y \mid \{R(X_1),X_2\}...
Hepdrey's user avatar
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2 votes
1 answer
118 views

Borel-Cantelli lemma on conditional probabilities

In a probability space $\big( \Omega, \mathcal{F}, P \big)$, suppose $\{E_n\}_{n\in \mathbb{N}} \subseteq \mathcal{F}$ is a sequence of mutually independent events. By Borel-Cantelli Lemma, the ...
Sanae Kochiya's user avatar
2 votes
1 answer
85 views

How to come up with an example that $E(\epsilon|z,\eta)=E(\epsilon|\eta)$ and $E(\epsilon)=0$ do not imply $E(\epsilon|z)=0$?

I'm trying to come up with an example showing that $E(\epsilon|z,\eta)=E(\epsilon|\eta)$ and $E(\epsilon)=0$ do not imply $E(\epsilon|z)=0$. The model is nonparametric IV model with the structural ...
Ludwig Gershwin's user avatar
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0 answers
11 views

Would a time series of sentiment valued between 1 and -1 be independent observations?

I am going through a course on linear regression and they say to check for independent observations: "based on the data collection process would the value of one data point impact the value of ...
professional pidgon's user avatar
3 votes
1 answer
31 views

Why do we make a time series stationary if the ARIMA, AR and other models are clearly working with the dependence of lags?

When we run a AR model, we are using a linear combination of its lags to predict the current value. So this means that the lags are related to each other (at least t-1, t-2, ..., t-n are related to t0)...
Andrew Joplh's user avatar
0 votes
0 answers
13 views

Test for independence of multivariate normality in R

I have 3 normal data matrices, i.e., that in each matrix, the rows are iid Multivariate Normal, but the rows of different matrices need not be identically distributed, but they have the same dimension....
Shaikh Ammar's user avatar
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0 answers
14 views

Dependent variable as a ratio [duplicate]

I have a dependent variable that is a ratio of how many investments in a year were made in a certain industry. So e.g. the firm made 4 investments and two of those in the technology sector which would ...
lazer's user avatar
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2 votes
0 answers
46 views

Confidence intervals for proportions and independence

Suppose a company sells various products at different prices. I would like to compute confidence intervals for the contribution of each product to overal sales, preferably in terms of currency (e.g., ...
cthl's user avatar
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1 vote
1 answer
63 views

Can I fit distribution of pixel intensity?

I have an image and I want to plot the histogram of pixel intensity. The distribution seems a Poisson distribution (long tail). Can I fit this distribution using matlab function ...
HelpNeederStudent's user avatar
0 votes
0 answers
28 views

Distribution of conditional independence

I have random variables W,A,Z,U and know that the following conditional independence holds: $W \perp (A,Z)|U$. Is it correct to then state that $W|ZA\sim W|U$? My reasoning is the following but am ...
MarsRooover's user avatar
2 votes
1 answer
28 views

Independence of real and imaginary part of the product of two independent normal variables

Let $X_1,X_2,Y_1,Y_2$ be iid standard normal variables $N(0,1).$ Let $X=X_1+iX_2,$ $Y=Y_1+iY_2$ and $Z=XY.$ We have : $Z=(X_1Y_1 - X_2Y_2) + i(X_1Y_2 + X_2Y_1).$ From https://en.wikipedia.org/wiki/...
fbrx's user avatar
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1 vote
1 answer
48 views

Standard error calculation for difference in means

In the case of two independent samples, the formula for standard error of the difference in means is given by : $$\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}$$ Even though we are talking about a ...
Happy Cretine's user avatar
0 votes
0 answers
9 views

Sampling: when is multivariate random variable interpretation dissimilar to repeated realization of single random variable interpretation

After reading many different posts on this site regarding the relationship between random variables and samples, I still have one lingering question (my apologies if I've missed any post explicitly ...
S.C.'s user avatar
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0 answers
8 views

What is meant by the assumption of statistical independence among sources in Independent Component Analysis?

One of the underlying assumptions of independent component analysis (ICA) that I consistently see written is "statistical independence across the source signals". In the context of the ...
S.C.'s user avatar
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2 votes
0 answers
21 views

When are mean and variance estimates uncorrelated or independent

I know that in the case of the normal distribution, the MLE estimates of the mean and the variance are independent. My impression is that this is a rare property for a distribution to have. Are there ...
Snildt's user avatar
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0 votes
0 answers
43 views

How to calculate the expectancy of the ratio of non-independent random variables?

How can I calculate this expectancy: $$ E \left [ \frac{\sum_{t=1}^T{Z_tX_t}}{\sum_{t=1}^T{Z_t^2}} \right ] $$ where $Z_t \sim N(0,1)$ and $X_t \sim N(0,1)$ are independent? Any tricks? Is it ...
PaulG's user avatar
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0 votes
0 answers
13 views

U -statistics for bi variate sample problem

Let $(X_1, Y_1), (X_2, Y_2),....,(X_n, Y_n)$ be iid random variables with joint distribution function $F(x, y)$ and $F(x), G(x)$ be the marginal distribution functions of $X_1$ and $Y_1$ respectively. ...
user771946's user avatar
6 votes
1 answer
498 views

Does independence almost everywhere imply independence?

Let be $X$ and $Y$ two random variables such that, for any event $A$, $P( X \in A \mid Y) = P(X\in A)$ with probability 1. Can I conclude that $X$ and $Y$ are independent ?
Pohoua's user avatar
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0 votes
0 answers
54 views

PMF of the Independent Multivariate Bernoulli Distribution

I was reading this paper on the Multivariate Bernoulli Distribution, which provides the general form of the PMF in equation 3.1. The paper refers to this as the probability distribution function, but ...
nka5we's user avatar
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