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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1answer
33 views

Central limit theorem for the function of an iid random variable

Given an iid random variable $X$, instead of the distribution $\sqrt{n}(n^{-1}\sum{X_{i}}-E[X])$ which is the result that the central limit theorem provides , I am interested in the distribution of $\...
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What happens if I use OLS in a multiple (hedonic) regression where prices are systematically missing?

I am using a hedonic regression of (log) housing prices on a set of price-determining characteristics. I then use the estimated coefficients to estimate housing prices for observations not in my ...
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1answer
27 views

Definition of independent events in probability theory (Wasserman)

In Wasserman's "All of Statistics" p.26 he gives an example of an "independent event" as "flipping a fair coin twice", where the first flip has no effect on the second ...
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14 views

Example of two Random variables which are independent but from different distributions [duplicate]

I was reading about meaning of iid(independent but with identical distribution). Can there exist some 2 random variables which are independent but from different distributions? Any example?
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32 views

Are stationary markov chains iid random variables?

Let $\{X_t\}_{t=1}^{\infty}$ be a Markov Chain. An initial marginal distribution $\pi^T$ for a markov chain is a stationary distribution if $\pi^TP = \pi^T$. My understanding of this is that if the ...
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35 views

Machine Learning IID [duplicate]

I am new in ML so excuse me if this is a bit basic. I noticed many times that the requirement for some methods in ML is that the instances are IID(e.g. Stochastic Gradient Descent). I don't exactly ...
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45 views

i.i.d assumption: formal definition vs. intuition [duplicate]

Intuition In ML, as I constantly run into the i.i.d assumption for datasets, I have an intuition of what this assumption really means. So if I'm not mistaken: "independent" means that ...
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30 views

Is there any need of random sampling for IID Data?

I understand that random sampling is required for the purpose of creating an unbiased sample with the same characteristics as the population. I am confused about whether random sampling is required ...
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25 views

Iid random variables with infinite variance are unbounded

While preparing for an exam I've stumbled upon an exercise I have no idea how to approach: $X_1, \dots, X_n$ are iid random variables with $E(X_1) = 0$ and $V(X_1)=\infty$ Show that $\mathbb{P}(\{ |...
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1answer
46 views

Confounding variables VS i.i.d assumption

I made up an example so as to illustrate my question with some more context. Say there are two national parks, and a ranger is interested in finding out how the number of rabbits (Y) varies with the ...
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What is the expectation of $\left\langle (n \bar{y})^4 \right\rangle$, if $y_i \sim \mathcal{N}(\mu,\sigma^2)$? [duplicate]

Let $y_i \sim \mathcal{N}(\mu,\sigma^2), \; i = 1,\ldots,n$ and $\bar{y} = \frac{1}{n} \sum_{i=1}^n y_i$, such that $n \bar{y} = y_1 + \ldots + y_n$. Then, we want to know what the expectation of $(n \...
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When can we reasonably assume a sequence of r.v.'s is IID in real life scenarios? [duplicate]

When can we reasonably assume a sequence of r.v.'s is IID in real life scenarios? My question is based off the following example from Wasserman's All of Statistics: Suppose we test a prediction ...
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2answers
164 views

Summation of i.i.d. Normal Random Variables

Assuming I have $$X_1,X_2,...,X_{100}\sim N(1,4)$$ and $$Y_1,Y_2,...,Y_{20}\sim N(2,9)$$ where all $X$ are iid, all $Y$ are iid. Then should $$\text{var}(X_1+X_2+\ldots+X_{100}+Y_1+\ldots + Y_{20}) = ...
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1answer
41 views

The non i.i.d. problem resulted from active learning query strategy

We usually assume the i.i.d. assumption in machine learning problems, but in active learning, the labeled examples acquired by querying oracle are clearly not i.i.d. I want to know will it be better ...
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1answer
31 views

E[X/Y], iid, show it is greater than 1 [closed]

X, Y are IID. show E[X/Y] > 1.
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Finding a sub-population from dataset matching another target dataset

Let's say one has a finite collection of i.i.d. samples from an unknown source distribution $S=\{x_{i} | i \in [1,n_{S}], x_{i} \sim p_{X_{S}}(x)\}$. Where each $x$ is multidimensional and has ...
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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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27 views

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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1answer
59 views

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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1answer
50 views

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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2answers
118 views

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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1answer
44 views

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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183 views

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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1answer
67 views

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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1answer
145 views

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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50 views

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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19 views

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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1answer
187 views

When using a gaussian link in GLM, what are the assumptions?

In R, when I am fitting a model glm(y~x, family = gaussian(link="log")), do I assume that $Y \stackrel{iid}\sim N(\mu, \sigma^2)$ or do I assume that $Y \stackrel{...
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146 views

How to compute ESS (Effective Sample Size)?

I implemented the ESS calculation according to this manual like this: ...
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What if my samples are not IIDs? [closed]

I'm testing my system and getting some results over time (Queues size, wating time, ecc.). When I plot the correlograms they exhibit a high degree of autocorrelation, even for high lags. Now, what are ...
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What exactly is $p(x,y)$ in the context of iid assumption in machine learning?

In machine learning iid assumption means that examples in the dataset are independent and drawn from the same probability distribution (i.e., identically distributed). Here, the probability ...
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Realistically, does the i.i.d. assumption hold for the vast majority of supervised learning tasks?

The i.i.d. assumption states: We are given a data set, $\{(x_i,y_i)\}_{i = 1, \ldots, n}$, each data $(x_i,y_i)$ is generated in an independent and identically distributed fashion. To me, ...
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2answers
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Clarifying the meaning of i.i.d. when describing a set of variables

Let $Z_1, ..., Z_k$ be identically and independently distributed (i.i.d.) set of standard normal random variables. I understand that as part of the i.i.d. independent broadly means that variables ...
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Shouldn’t we say independent given the distribution?

In statistics we often deal with iid random variables: independent identically distributed. But if we don’t know the distribution (say we still know the support is {0, 1}), and we get a sample x1, say ...
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1answer
358 views

Why is the MLE for variance in single linear regression biased? [duplicate]

I understand that the Maximum Likelihood Estimator for variance, in general, is biased (the average calculated from the sample itself reduces the degree of freedom by 1 e.t.c): ...
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449 views

Probability that one positive random variable is greater than another independent and identically distributed positive random variable

Suppose I have the following random variables $X_{0} \sim f(x)$ and $X_{1} \sim f(x)$ are independent. I want to know the probability that $X_{0} > X_{1}$. So I think I want to find: $$ P(X_{0}>...
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1answer
593 views

Probability of a machine failing when components fail independently

Our machine is made out of 3634 units of component A which has failure rate of 10%, 1656 units of component B with failure rate of 35% and 3368 units of component C with failure rate of 55%. Assuming ...
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1answer
522 views

UCB Exploration in Reinforcement Learning

I have two questions regarding the upper confidence bounds (UCB) exploration in reinforcement learning: UCB exploration is derived from Hoeffding's inequality which assumes that the reward is bounded ...
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0answers
80 views

Bootstrapping regression coefficient for time series

One of the fundamental assumptions of bootstrap is that the samples are independent and identically distributed (i.i.d). This is the reason why it is difficult to bootstrap time-series because the ...
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2answers
632 views

Random Variable with IID always Gaussian?

Is there a case when we assume a random variable $\epsilon$ to be IID and assume its distribution is not gaussian?
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How to check Gauß-Markov theorem after OLS estimation?

I have estimate a simple bivariate regression with OLS and want to proof if the estimator is unbiased. I found that the Gauß-Markov theorem consists of 4 Assumptions and the first 3 can be rewrite as ...
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1answer
184 views

Expectation Value of a Product of Many IID variables

First of all, I apologize for not being rigorous, but I am not a statistitian by background. Imagine you have $N$ i.i.d. positive random variables $X_1...X_N$ and you are trying to compute a ...
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4answers
493 views

Check if residuals are IID (timeseries)

How can I check in R after decomposing a time series if my residual component is IID noise? Would this be the best way (to use the autocorrelation function) and check for 0 correlation on all lags > ...