# Questions tagged [iid]

iid is an acronym for independent and identically distributed. Many statistical methods assume that the data are iid; that is, that each observation comes from the same distribution and is independent of other observations.

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### Determine Expected Value and Bias of Gamma Distribution [closed]

Let $X_1,…, X_n$ be a sample of $iid$ $Gamma(4, 𝜃)$, and let $T = \frac{1}{4} \overline{X}$ be an estimator of $𝜃$. Determine: a) $E(T)$ b) $Bias(T;𝜃)$ c) $MSE(T;𝜃)$ d) whether $T$ is an MSE-...
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### Estimators that relate model accuracy to data distributions

Consider a set of dependent variables $D$, set of independent variables $I$ and $O_1, O_2,\ldots,O_N$ observations of these variables. The dataset is short and wide, $|D| = 3*N$. For each $j \in I$, ...
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### Does permutation test require iid?

Suppose I have a treatment group X and independent from control group Y. The data set x1,x2..., y1,y2... Let's say I want to test the mean of the difference If the randomization unit is a session ...
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### Transfer Learning: data in the source domain and the target domain are required to be independent and identically distributed

In instance-based transfer learning, it is said that data in the source domain and the target domain are required to be independent and identically distributed. When it says that the data "are ...
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### Independent and identically distributed data (images)?

If it is said that the data must be independent and identically distributed, and the data are images, then what exactly does it mean for images to be "independent and identically distributed"...
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### Does a version of the Delta Method exist for non-i.i.d. sequences?

I have a sequence of random variables that are non-independent, but usually identically distributed. I am wondering if a version of the Delta Method exists under the case when I only have that the ...
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### Expected vallue calculation of i.i.d. random variables

Suppose $X_1,X_2,\ldots,X_n$ are a sequence of i.i.d. random variables with mean $\mu$ and variance $\sigma^2$. Define the sample mean $\bar{X} := \frac{1}{n} \sum_{i=1}^{n} X_i$, which we know is an ...
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### How do you compare samples if they are not Independent and Identical Distributed (IID)?

I have 2 questions. Nr. 1: I have a simulation model running for 1 year (after the warm-up period) that simulates the patients coming into a clinic for their treatment (set up daily) (a patient may ...
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### What does i.i.d. mean for multivariate case?

When we say a random variable is i.i.d., it's often used to describe the dependency between the observations of that random variable, which I call the row dimension, indexed by time if it's a time ...
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### Is there a central limit theorem for random variables with a bounded interval? [duplicate]

Is there any theorem which states the asymptotic distribution for the sample mean when the samples are drawn from a random variable which has a bounded interval?
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### What is a random process with “stationary independent increments”?

I'm looking at a Solved Problem in "Schaum's Outline: Probability, Random Variables, and Random Processes", specifically Problem 5.21. In this problem it states: Let $\{X(t), t \ge 0\}$ be ...
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### How are cross validation and i.i.d. assumption of of a dataset related?

Is it necessary for the observations of the data set to be IID in order to use cross-validation on it? If so, why ? Could you explain in the context of a classification using decision tree.
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### Apply panel data techniques to a panel where observation can be assumed to be independent?

I'm working with a data-set and am unsure if I should apply specific panel data techniques to it or not. The data consists of panel data for municipalities in the Philippines and damage cause to rice ...
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### Is a sample i.i.d or is a collection of random variables i.i.d.?

Basic terminology question. I hear “let the sample be i.i.d.“ and “let these random variables be i.i.d.” being used interchangeably. Even Wikipedia uses both: A collection of random variables is ...
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### Does the mean preserving spread of a distribution constitute a mean preserving spread of the joint distribution of two iid draws from it?

Let random vectors $X_1, X_2 \sim F, \;i.i.d, X_1, X_2 \in X$. Now replace $F$ with its mean-preserving spread (MPS), say $G$. My question is, does that constitute an MPS of the joint distribution of ...
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### Accept-reject and subsets of iid samples

I have some confusion about subsets of iid samples being distributed as the original sample. As an illustration, consider the accept-reject algorithm to produce iid samples from a pdf $f(x)$. We draw,...
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### How to derive this MAE error bound on the central limit theorem?

Is this derived from Chebyshev's inequality or a tail bound theorem? If not, how was it derived? Does this require the existence of the third moment? Does this bound suggest the normal approximation ...
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### I.I.D. for the layperson? [duplicate]

Question: For the layman, what does it mean for data (say $n$ samples covering $m$ variables) to be identically distributed, and how is it practically achieved when conducting machine learning? So ...
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### Is a non-iid process necessarily a Markov Process?

This may be a silly question, but I've been wondering if a a random variable is said to follow a non-iid process, does that necessarily imply that it follows a Markov process?
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### Are feature values random variable realizations, or random variables themselves?

I'm new to ML/stats so got confused with what I supposed was simple notation. For simplicity, say I have a data set with just one column: From probabilistic perspective, I had understood that X ...
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### Is MLE intrinsically connected to logs?

My mathematical exploration led me the following claim: Claim: MLE is fundamentally connected to logs (and KL divergence, which also uses logs). It’s not correct to say log shows up simply to make ...
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### Functional data analysis references

I am working on a inferential framework for functional data. I have categorical independent variables and a functional response variables. Different implementations of functional linear models are ...
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### Does joint IID imply marginal IID?

Suppose you have a 2 dimension random vector denoted $(X,Y)$ that is Independent and Identically Distributed (IID) for a sequence of draws $((X_1,Y_1),(X_2,Y_2),...,(X_n,Y_n))$. Does this imply that ...
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### Calculate the variance of $\sum\limits_{i=1}^{n-1} \sum\limits_{j=i+1}^n S(X_i - X_j)$ for $X_1,\ldots,X_n$ i.i.d. random variables

In p.88 of Wand & Jones (1995), they asked to show the following result. Let $X_1,\ldots,X_n$ be a set of i.i.d. random variables and define U=2n^{-2}\sum_{i=1}^{n-1} \sum_{j=i+1}^n S(X_i - ...
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### Identically distributed vs P(X > Y) = P(Y > X)

I've two related propositions which seem correct intuitively, but I struggle to prove them properly. Question 1 Prove or disprove: If $X$ and $Y$ are independent and have identical marginal ...
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### What final test to apply to a permutation test (by compression) algorithm?

I'm following in the steps of §5.1 Permutation Testing, NIST Special Publication 800-90B, Recommendation for the Entropy Sources Used for Random Bit Generation. I'm developing my test for ...
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### Likelihood when points aren't i.i.d

If we assume that we have a set of N data points given as $\textbf{X}$ and corresponding targets vectors $\textbf{T}$, where both represents matrices in this case. For an i.i.d we could write the ...
Let $X_1, X_2, \dots$ be a sequence of independent and identically distributed discrete random variables with common mass function $f_X(x)$ defined for when $x \in \{0,1,\dots,N\}$ and $N$ is known. ...