Data, events, processes, etc, are non-independent if knowledge of 1 provides some information about the state or value of the other.

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43 views

Compare differences in dependent frequencies

I would like to compare two error rates (proportion of incorrect answers in questions with dichotomous response-format) for two different items, and I am looking for some advice on how to do that. ...
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1answer
55 views

Assume (x,y) are drawn from independent & identical distribution when y=f(x)

Sometimes we say the following: $X$ is some training data given by $X:=\{(x_1,y_1),...,(x_l,y_l)\}\subset R^d \text{x}R$. Assume that the training data had been drawn from independent and identical ...
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0answers
44 views

joint distribution, probability, calculating probabilities under false independent assumption, when the random variables are actually dependent

Suppose I have random variables $X,Y,Z$ and I would like to compute the probability that random variable $X$ is smaller than $Y$ and $Z$: $$ \pi_X \overset{def}{=} Pr(X < Y, X < Z) = \int Pr(x ...
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1answer
36 views

Using random forest for survival analysis with time varying covariates

I've been trying to train a model that predicts an individual's survival time. My training set is an unbalanced panel; it has multiple observations per individual and thus time varying covariates. ...
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3answers
61 views

Cox Models treatments depending on time until event

I'm trying to get the "productivity" of treatments like sending an email, calling or sending an SMS and their combinations in the paying debtor's probability. I couldn't find one model that satisfies ...
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1answer
52 views

How can I evaluate the probability density function of $Z=X+Y$,if $X$ and $Y$ are not independent?

If $Z=X+Y$, and the PDFs of $X$ and $Y$ are both functions of a deterministic variable $d$, how can I evaluate the PDF of $z$ while the convolution cannot be used here (due to lack of independence)?
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1answer
58 views

What are the implications of estimating a covariance matrix from a correlated sample?

Given a sample of $n$ independent observations $x_1,...,x_n$ (where $x_i$ are $p$-dimensional column vectors), the $p \times p$ sample covariance matrix is defined as ...
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1answer
61 views

Estimation based on observing sum of two variables

Let $X_1,\dots,X_n$ are i.i.d normal $N(\mu,\sigma^2).$ Suppose that we only observe $$ X_1+X_2,\dots,X_1+X_n,\dots,X_{n-1}+X_n, $$ i.e, $X_i+X_j$ for all $i<j.$ I wish to find the best estimator ...
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0answers
33 views

Estimating of variance of dependent normal distribution

Let $X_1,\dots,X_n$ are independent and identically unobservable variable on $\Omega$. Suppose that $f:\Omega\times\Omega\mapsto \mathbb R$ be unknown function such that we know the value of ...
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0answers
31 views

Expected value non-independent random variables

Let $X$ be a set of costumers, {$x_1, ..., x_N$}, each $x_i \in X$ have a discount $p_i$ in the interval $[0,1]$, it means if $p_i$ is 0.3, $x_i$ will pay only 0.3 of the entire value. I want to know ...
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0answers
33 views

Expected value of a function that is not sampled uniformly

How can I calculate the expected value of a random variable $R(\Omega)$, when the samples are not i.i.d? In my specific case, I have more samples at lower values of the parameter of the function, ...
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1answer
38 views

1-Way ANOVA with single independent/repeated (within/between) factor

I want to perform an ANOVA on data with a single factor with three levels. The difficulty for me is that two of the levels are repeated measures (within subjects) and the third level is independent ...
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0answers
15 views

Expectation of ratio of functions of Bernoullis: a concentration question

Consider the following $n \times n$ symmetric matrix of i.i.d. Bernoulli random variables, $X_{ij}$. For $i=1,...,n$ and $i<j\le n$. Let $X_{ij} \sim \text{Bernoulli}(p)$ when $i \ne j$, and let ...
2
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1answer
38 views

Does $P(B|A) \neq P(B| A^c)$ prove dependence?

Does P(B|A)!=P(B|!A) prove dependence? != means 'is not equal to' !A means 'not A' or 'the complement of A' Thanks. Edit: I believe I may have proved that inequality shows dependence. Proof: ...
2
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1answer
22 views

Dependent chi-squares vector: how to calculate cdf of $X_{(n)}$?

Consider a vector of central&1-degree Chi square distributed variable $(X_1, X_2,...,X_n)$, it is simple to calculate the cdf of $X_{(n)}$ (maximum of order statistics), when they are independent. ...
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1answer
84 views

chi-squared test when variables dependent

For a square matrix, is it appropriate to use a chi-squared distribution when each level of the variables are assumed to have the same overall frequency? Specifically, I'm analyzing a dataset of the ...
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0answers
28 views

Correlation between non-independent variables

I want to conduct correlation between two variables, that have common term (difference scores). Originally there are three variables X, Y, Z. I want to conduct correlation between two variables that ...
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0answers
40 views

Are these distributions independent?

I'm trying to compare the medians of two non-normal distributions: $A$ and $B$. $A$ is the distribution of completion durations for one type of task $B$ is the distribution of completion durations ...
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0answers
20 views

How to eliminate dependent inputs?

There are a lot of statistical methods that rely on the assumption of input independence. For example, Naive Bayes text classifiers operate under the assumption that occurrences of different words are ...
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0answers
25 views

ANOVA and dependence WITHIN a group

I have three different methods that I would like to compare using ANOVA. The variable to compare is method accuracy that I get trough cross-validation. This means that the same data set (N=60 ...
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1answer
17 views

Integrating multiple tests Bayes factors

I have been using an Bayesian-centric R package for some genomics analysis to detect mutations in 3 individuals from the same family. I have to do each analysis for each individual separately due to ...
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0answers
34 views

Variance-covariance matrix as the sum of variance covariance matrices

I have a variance-covariance matrix, $\mathrm{V}$. This allows me to take a vector, $x$ of independent random variables drawn from a known distribution, and induce a required variance-covariance ...
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2answers
26 views

GLMM for SNA and non-independency data

I contact you because my case is particular and I don’t know much about GLMM. I have data of social networks (network metrics) of a nonhuman primate species. These data are by nature non independent ...
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0answers
44 views

Extremal serial dependence

As part of my analysis of heavy-tailed time series of company returns, I would like to check whether extreme returns exhibit serial dependence, i.e. if extreme events are followed by extreme events. ...
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74 views

Analysis for cross-subjects correlation

Suppose that an investigator has collected some longitudinal data from each of the $n$ subjects, and that a correlation coefficient is computed on the data between any pair of subjects, leading to ...
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3answers
166 views

Best method to predict binary outcome with multiple records per subject

I am interested in building a model to predict the binary outcome, retention (1 - retained; 0 - not retained) with various potential predictor variables (either continuous or categorical). With that ...
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0answers
41 views

Probability of vector similarity wrt dimensionality

I'm trying to show that the probability that two vectors are similar to each other increases as the number of dimensions decreases. I define similarity between two vectors $a = [a_1, a_2, ..., a_n]$ ...
2
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1answer
176 views

Statistical Power of ROC/AUC Test with non-IID Samples :: To how many IID Samples are my non-IID Samples Equivalent?

I've been assigned to solve the following problem as part of a serious, biological research project. I think I have a tentative solution, but I'm wondering whether the approach I've picked is the ...
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1answer
112 views

Sum of Dependent Poisson Random Variables

I am working with the distribution of the sum of two dependent random variables. In my problem, there are two unobserved events, X and Y, where X precedes Y and Y is a function of the outcome of X, ...
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3answers
83 views

A critical proof or counterexample regarding independence

Does independence of $X^2$ and $Y^2$ imply independence of $X$ and $Y$?
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1answer
45 views

Correlation and dependency of two variables

Lets say I am interested in finding the correlation of the following two metrics. They are aggregations and include the same input A in their formula. Is it possible to talk about correlation of ...
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30 views

When is the determinant of a covariance matrix is 0? [duplicate]

Any covariance matrix $A$ must be non-negative definite or semi-positive definite. This means that its deteraminant should always $|A|\ge0$. In case $|A|=0$, what would happen? or what does this mean ...
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1answer
53 views

When is the IID Assumption too strict for the bootstrap?

The Bootstrap (Efron 1979) assumes that the data are IID. Obviously, if we have time series data then we probably cannot make that assumption unless we have a special case that we a time series of ...
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0answers
58 views

Random effects and repeated measures: what would you choose as random effect?

I have a question regarding the use of random effects in order to account for a violation of the assumption independent samples. I have this discussion with my supervisor and we disagree about this ...
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1answer
49 views

confidence intervals for dependent observations

The answer to this question discusses problems associated with calculating P-values for dependent observations. Let's say you have observations from two different groups that are dependent. You ...
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1answer
67 views

DNA: The number of 'AAAAA'-s in a randomly generated DNA sequence that's 1000 base pairs long

Let's say I have a randomly generated sequence consisting of letters A, C, T and G that's 1000 letters long. The probability of each letter occurring is 25%. What is the probability that the sequence ...
2
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1answer
147 views

required: good and straightforward method to detect change points in dependent univariate time series using r

I know that there are many related threads, packages and papers. Currently I`m reading through many of them. However, I don't plan to dig too deeply into this topic. I need a sound method that works ...
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0answers
108 views

Why doesn't correlation of residuals matter when testing for normality?

When $Y = AX + \varepsilon$ (i.e., $Y$ comes from linear regression model), $$\varepsilon \sim \mathcal{N}(0, \sigma^2 I) \hspace{1em} \Rightarrow \hspace{1em} \hat{e} = (I - H) Y \sim \mathcal{N}(0, ...
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2answers
72 views

data representation with nominal, ordinal and continuous variables

Suppose I have data of this format: customer, country, location, unit price, traffic, etc. (more nominal/ordinal variables) I want to know how country affects unit price, how do I go about doing ...
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0answers
45 views

What exactly is a higher-order correlation? [closed]

What exactly is a higher-order correlation? Is the term just a catch-all for all dependencies that are not captured by second-order correlations? Or do people mean something more precise than ...
2
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1answer
68 views

Chi-square test to see if set of dependent correlations are equal

I've got four dependent correlations (i.e., from the same sample) that involve predictor variables $(A,B,C,D)$ and an outcome variable $(E)$. $N=172$. $$\begin{array}{c|cccc}{\rm ...
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0answers
28 views

Test which method is better if data is gathered on overlapping time windows (not independent)

I have two methods which are being used to estimate a specific signal. I have a ground truth measurement of this signal and these two methods are using noisy data to estimate this signal. This signal ...
2
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0answers
23 views

Estimating distribution function for dependent observations

Let $X_1,\dots,X_n$ be identically but not necessary independent distributed with distribution function $F$. I'd like to estimate $F$ efficiently. In case, $X_1,\dots,X_n$ are i.i.d., we can estimate ...
5
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1answer
141 views

Overlapping sample t-test

I have 10 people working together. They work in groups for 6 days: Three days in week 1, three days in week 2. In each day I don't have the full set of people, but a subset of them. In each day I ...
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0answers
45 views

Correlation between predictor variables and time in Survival Analysis?

I am using survival analysis to model time to an event. I would like to explore the effect of a continuous predictor variable on the hazard rate. The continuous predictor ranges in value from 0-8.5. ...
0
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0answers
140 views

How do I test the difference between two dependent correlation coefficients whilst controlling for other variables?

How do I test the difference between r(X,Y) and r(X,Z) [Williams Test?] whilst controlling for demographic variables that were measured in addition to X and Y and Z [Partial Correlation]? Thanks, ...
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40 views

Neural Network, dependence among outputs?

Is there a way to train a neural network in the following manner: You have $n$ observations in the training set. The neural net will start with random weights, and produce $n$ outputs. I want to ...
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0answers
32 views

Is the multivariate Gauss the only pdf incorporating covariances?

I am wondering whether there is another probability density function known to literature which is similar to the multivariate normal distribution in the respect that the pdf incorporates the ...
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1answer
84 views

What are $\rho$-, $\beta$-, and $\alpha$-mixing conditions?

I have seen properties named $\rho$-, $\beta$-, and $\alpha$-mixing conditions in papers related to Copulas and Markov processes like this one: In this paper, we identify conditions on $C$ that ...
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1answer
42 views

Independent vs. Dependent Compound Poisson Distributions

I have an issue with a section of some Actuarial lecture notes that I am reading. Here are the snippets from the notes: "Consider a portfolio consisting of $n$ independent policies. The aggregate ...