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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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T-test - sample test - group statistics. Can I make a conclusion of this if my sig (2-tailed) is not significant? [on hold]

my hypotheses were 1) lower comprehending score for living out of the home, 2) higher distancing score for living out of home. The group statistics do show that my hypotheses were right but the ...
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0answers
16 views

T-test - (2-tailed) is not significant? What conclusion can I make from this table? [on hold]

My hypothesis was: 1_ Higher comprehending score for mothers vs fathers 2_ No difference on distancing score for mothers vs fathers My teacher did the SPSS part so I'm not exactly sure if this ...
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0answers
12 views

Can i assume independence after adjusting for cross correlation in an event study?

I'm doing an event study on rebalancing date of an index. The rebalancing happens every quarter. Using 50 tickers this implies i have multiple events on the same ticker, which is fine, but since it ...
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0answers
53 views

Stuck on a term in $\operatorname{Var}\left[ \widehat{\beta}_0 \right]$ proof

So I was trying to prove that $\operatorname{Var}[\hat{\beta}_0] = \dfrac{\sigma^2n^{-1} \sum{(x_i)^2}}{\sum{(x_i-\bar{x}})^2}$ And I got stuck with the part $\dfrac{-2\bar{x}}{\sum{(x_i-\bar{x})^2}} ...
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0answers
18 views

$X$ independent of $Y$ conditional on $Y$ in some subset of the domain?

Let $X,Y,\epsilon:\Omega\to \mathbb R$ be random variables. Let's say that $X=\text{sign} (Y) +\epsilon$. Then $X$ is not independent of $Y$. However, we have all the information about $Y$ that we ...
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1answer
25 views

Violation of independence or still valid?

I have to test the the effect of two different treatments on a set of samples. On the surface, this seems an obvious option for a two sample test. The problem is that the samples being treated are ...
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1answer
25 views

Sampling from specific distribution

Suppose I have two random variables $X$ and $Y$ that are independent. Also suppose that I can sample from $X+Y$ and $Y$. Is it possible to combine those two sampling algorithms to get samples for $X$.
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1answer
59 views

multivariate Student's t distribution: intuition for non-independence?

Consider a multivariate Student's t distribution, with parameters $\nu$ (d.f.), $\mu$ (location) and $\Sigma$ (shape). Does anyone have a good intuition for the individual components not being ...
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0answers
10 views

Non-independence of bootstrap samples

Background Suppose we have a dataset that consists of $n$ iid random variables represented as $X_j$, where $j \in \{1,\ldots,n\}$. We know $\forall i,\, \operatorname{E}\left(X_i\right) = \mu$, and ...
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0answers
7 views

Survival Statistics Independence

If we observe follow-up times Ti = min(Xi,Ci) and right censoring indicators δi = I(Xi ≤ Ci) under noninformative censoring. Is Xi independent of δi? Please explain why, thanks!
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2answers
74 views

Difference between independence and stationarity tests in time series

This is meant to be a general question, aiming to clarify the topic for a beginner in TSA, as I haven't found any clear introductory explaination yet. Suppose I am working with some data which ...
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3answers
59 views

How to determine if two categorical variables are dependent while controlling for a 3rd categorical?

I have 3 categorical variables: country, gender, and liked (whether the user liked the content or not). Using Chi-squared I see that 'liked' is dependent on country, that 'liked' is dependent on ...
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1answer
30 views

sampling distribution using normal and rectangular distribution

Let $X_1,X_2$ be i.i.d. $N(0,1)$ and $U_1,U_2$ be i.i.d. $U(0,1)$ and independent of $X_1,X_2$. Define $$Z_1=\frac{(X_{1}U_{1}+X_{2}U_{2})}{\sqrt{U_{1}^2+U_{2}^2}}.$$ Find the distribution of $Z$. ...
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1answer
21 views

Can pieces of evidence that arise from different aspects of the same phenomenon be independent?

Say I want to know whether my roommate is baking a pie. When she bakes, she tends to hum songs. When she bakes, I tend to smell it happening. When she bakes, I tend to see her less in the living ...
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0answers
23 views

Questions about tail dependence of copula and copula parameters?

I would like to understand tail dependence and its relationship to the copula function. The relationship between copula and tail dependence can be expressed as: (from this question Understanding ...
2
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0answers
28 views

A symmetric iid process

Let $X_1, X_2, \ldots$ be an iid process with $X_i$ having a symmetric distribution around $0$. Then can I always write $$X_1 - \alpha X_{t-1}-\alpha^2 X_{t-2}-\cdots \stackrel{iid}{=} X_1 + |\alpha| ...
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0answers
51 views

Showing that two random variables are independent [closed]

If $f(x,y) = g(x+y)$ with $0 \leq x,y \leq 1$ and $0 \leq x+y \leq 1$ then are $X$ and $Y$ independent?
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1answer
20 views

Can ANOVA be used for percent frequency data?

Problem: Suppose there are three restaurants in a town. I conduct a survey by asking each person what percentage of time you eat in restaurant A, restaurant B and restaurant C. The percentages for ...
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0answers
44 views

Can i say an iid process with $0$ mean has homogeneous independent increment?

I think the title is itself self-explanatory. My idea says that an IID process with $0$ mean has to have independent increment. But, I do not understand how to prove homogeneity?
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1answer
24 views

Independence for chosen digits for binary numbers selection

Let us consider all binary $n$-digits numbers. Out of them, we choose at random $m$ distinct numbers. Denote by $Y_1,...,Y_n$ the number of the chosen numbers with the first digit 1, ..., the number ...
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1answer
32 views

Expected value of joint quantile functions

Consider a population of individuals (not a sample). We are interested in two variables, $X$ and $Y$, which are independent. $X$ distributes with pdf $f(x)$ and CDF $F(x)$, and $Y$ distributes with ...
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1answer
42 views

What are the possible tests for gauging the correlation between two categorical variables? [duplicate]

I have two categorical variables: Emotions {Sad, Happy, Neutral} and Psychological_state {Depression, Normal, None}. I want to interpret the relationship between these two variables (is there a ...
2
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1answer
39 views

Wilcoxon signed rank test independence assumption

Let us say we perform Wilcoxon signed-rank test on paired samples $x_{1,i}$ and $x_{2,i}$. I am trying to understand the independence assumption of the test. My questions are: Which quantities must ...
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0answers
22 views

Can I use mean of mean for a/b testing?

I want to design an A/B testing for the independent two-sample t-test. Assume I want to compare the number of items people purchased. group A is the control group, group B is the testing group where ...
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1answer
43 views

A special case of the law of large numbers for (possibly) dependent, identically distributed random variables

I want to show that $\dfrac{1}{N}\sum\limits_i^N x_iw_i \to 0$ as $N\to\infty$, where $w_i\sim \mathcal{N}(0,\sigma^2)$, $\mathbb{E}[x_i] = 0$ and $\mathbb{E}[x_i^2] = \rho$. The $x_i$s are ...
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1answer
100 views

If $X=Y+Z$ with known pdf of $X$, are $Y$ and $Z$ unique?

Say there are random variables such that $X=Y+Z$ with $Y$, $Z$ independent; knowing the pdfs of $Y$ and $Z$, one can (technically) find the pdf of $X$. Taking it from the other side: if one knows the ...
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0answers
20 views

Can two random variables, both of which are dependent on a 3rd random variable, be independent of each other?

Let's say we have three random variables X, Y, Z. We know that X and Y are dependent, and also that Y and Z are dependent. Under this setting, is it possible for X and Z to be independent? (...
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1answer
31 views

Inequality of two independent random variables

My question is related to this one but more specific. Inequality on two random variables We have two continuous random variables, $X$ and $Y$. We know that the expected value of both is 0 (or more ...
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0answers
12 views

How to minimize dependency between existing model and retraining dataset (using fraud modeling as example)?

What are methods to minimize dependencies between the existing model in production and the data that will be used for retraining future models (when future samples are created based on the existing ...
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0answers
25 views

What should I do about this regression analysis?

I did regression analysis. It's about incoming calls and amount of orders. I got a result like this. summary(ireg) Call: lm(formula = 1/sqrt(ie) ~ ia + id) Residuals: ...
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0answers
32 views

Panel data: Does a lagged independent variable as a regressor violates strict exogeneity?

A dynamic panel data model is considered in the sense that it contains (at least) one lagged dependent variable. Including a lagged dependent variable as a regressor violates strict exogeneity, ...
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0answers
33 views

Deterministic limit of “ML” and it's generalization to the non-deterministic case

I was told a few years ago at school (grad school) that for independent features the Naive Bayes classifier is very good, "almost perfect". Especially if we consider binary features because then the ...
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2answers
21 views

Validity of non independent observations in Poisson regression when modelling incidence rates

I have a question regarding fitting a poisson model to non-independent observations when assessing the incidence of an outcome. I am interested in the incidence of some outcome, O, over time. I have ...
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1answer
44 views

Covariance in terms of independent random variables

If I understood everything in statistics correctly, the covariance of two random variables should be given by $$\mathbb{E}[\phi(X_1)\phi(X_2)] = \iint \phi(x_1)\phi(x_2) p(x_1, x_2) \mathrm{d}x_1 \...
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0answers
21 views

Events/Trials Syntax vs. Single-Trial Mixed Model - Beta-Binomial Model

I'm a touch confused about modeling an events/trials outcome when the Bernoulli trials are not independent, such as when a series of Bernoulli trials are observed from the same person. I cannot find a ...
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1answer
26 views

Independence of multivariable function of random variables on the information

It might be this question was asked before, but I still want to request an answer in measure-theoretic framework. Let's define a probability space $\{\Omega, \mathcal{F}, \mathbb{P}\}$ and $\sigma$-...
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2answers
71 views

Regression assumption

I have a data set where $100$ people made $500$ trips for $5$ days. I want to build a trip-level regression (zero-inflated Poisson) where the dependent variable will be the count of hard-braking in ...
2
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1answer
332 views

When multiple realizations of uncorrelated but dependent random variables are added they become independent

I have empirically noticed and interesting phenomenon. Suppose we have two continuous random variables $X$ and $Y$ which are dependent but not correlated. For instance: $X \sim \mathcal{N(0,1)}$ $Y =...
2
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1answer
14 views

Hypothesis Test For Independence in Trials?

I had asked this question over on Math Stackexchange but I was wondering if could get any interesting feedback here as well (at the time of this question I haven't received an answer on Math exchange ...
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1answer
75 views

Can you explain this statement and mathematically verify if it's correct?

"“A nuclear attack is inevitable. It’s the ultimate problem of mankind. If there’s a ten percent probability that something will happen in a year, there’s a 99.5 percent probability that it will ...
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3answers
3k views

Does statistical independence mean lack of causation?

Two random variables A and B are statistically independent. That means that in the DAG of the process: $(A {\perp\!\!\!\perp} B)$ and of course $P(A|B)=P(A)$. But does that also mean that there's no ...
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0answers
27 views

Rss and sample variance indipendence in simple linear regression

Suppose that $ (X_1 ,Y_1...X_n,Y_n) $ is an i.i.d. random sample from a simple homoschedastic linear model $Y=\alpha +\beta X+e $ , with $e|X \sim N(0,\sigma_e^2)$. I want to understand if $ \frac{...
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0answers
8 views

Can the correlation matrix be justified to explore the linear independence of categorical variables on the response variable after the encoding?

I am investigating the independence of some categorical variables (apps, campaigns...) on the response variable (click through rate). Can the correlation matrix be justified to explore the linear ...
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0answers
25 views

Can Chi-Sq Test be used to explore the independence of categorical variables on response variable?

I am investigating the independence of some categorical variables (apps, campaigns...) on the response variable (click through rate). I have some doubts on using Chi-Sq Test here: Chi-Sq Test can be ...
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0answers
24 views

What is the covariance between X and Y, when $Y>0$ if $X<0$ and $Y<0$ if $X>0$?

Let $X$ and $Y$ be two random variables, and $Y>0$ when $X<0$ and $Y<0$ when $X>0$, but can we conclude Cov$(X,Y)<0$? If the question only states $Y>0$ when $X<0$, then the ...
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1answer
51 views

Maximum Likelihood Estimation IID Samples

According to these notes from Penn State on MLE and notes from Stanford CS229 on logistic regression, training data is assumed to be IID. The Penn State notes say "...which implies by definition that ...
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19 views

How to test for independence for a rate/probability measurement between two dimensions?

Say, we are working on Impressions and Clicks measurement, on two dimensions: country and age_group. And the following is our (...
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1answer
16 views

Independence test informs paired difference test in matched pre/post settings?

I have a, perhaps faulty, intuition that if a paired difference test (e.g., Wilcoxon rank sum, t-test) for a pre/post item looks significant, one should use caution in interpreting this fact if an ...
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0answers
23 views

Violation of Independence Sample

In almost all statistical testing, one assumption is that the sample is independent. But, the reality is that most time series data violate this assumption given that multiple events are generated ...
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3answers
112 views

Independence of statistics from gamma distribution

Let $X_1,...,X_n$ be a random sample from the gamma distribution $\mathrm{Gamma}\left(\alpha,\beta\right)$. Let $\bar{X}$ and $S^2$ be the sample mean and sample variance, respectively. Then prove ...