Questions tagged [iid]

Question 1

Given a sample $X_1,\ldots X_n$, how can I test the hypothesis that these are i.i.d. samples from a fixed (unknown) distribution? To add context, assume this is a time series and I want evidence ...

Question 2

In standard machine learning settings with cross-sectional data, it's common to assume that data points are independently and identically distributed (i.i.d.) from some fixed data-generating process (...

Question 3

I am working on a project analyzing olive plantation data, where I aim to simulate the relationship between investment costs (Costs), revenues (...

Question 4

Definition: Random variables X1, X2, ..., Xn are said to be independent and identically distributed (i.i.d.) if they are independent, and they have the same marginal distributions: FX1(x)=FX2(x)=...=...

Question 5

I was working through some econometrics problems, and my professor used the result that the product of iid random variables is iid, but I've seen some posts that this might not always be the case. My ...

Question 6

I would be interested in finding the value of the following expression: $$\mathbb{E}[X_k^2\mid S_N]$$ where $X_k$ are iid random variables with $\mathbb{E}[X_k]=\mu$ and $\operatorname{Var}[X_k]=\...

Question 7

Take: $X_i , \ i = 1, ... , n $ iid. $\varepsilon_i , \ i = 1, ... ,n$ also iid. $X_i \not \perp \varepsilon_j$ (they are not necessarily independent) Are $X_i \varepsilon_i$ iid ?

Question 8

There are numerous material that show the relationship between MLE and cross-entropy. Typically, these are the steps taken to show the relationship for a I.I.D data generating process $D = (X,Y)$: $$ ...

Question 9

I've read dozens on post on the subject but I cannot figure this out. From what I've gathered, GLMS don't include an error term in their formulation unlike linear models (LM). I was wondering why (or ...

Question 10

Given that all three iid rv’s ($X_1, X_2, X_3$) have CDF $F(x)$, the formula for the CDF $G(y)$ of the largest rv ($Y=X_i$) among the three is: $G(y)=P(X_1 \leq y) \cdot P(X_2 \leq y) \cdot P(X_3 \leq ...

Question 11

The method-of-moment of $\sigma$ for the following pdf is $$ \text{pdf}(x,\sigma) = \frac{x}{\sigma^2}\exp(-\frac{1}{2}\frac{x^2}{\sigma^2}) $$ $$ E[x] = \int_{0}^{\infty}\frac{x^2}{\sigma^2}\exp(-\...

Question 12

Generally, can repetitive patterns in sensor readings (e.g. temperature measurements at different locations over time) be seen as some kind of stochastic process? That is, if similar patterns repeat ...

Question 13

I was reading about an approach to Survival Analysis called "First Hitting Time Models" (threshold regression): https://www.jstatsoft.org/article/view/v066i08 , Can Survival Models model the ...

Question 14

Let $X_1,\cdots,X_n$ be (discrete in my case) i.i.d. and bounded between $m$ and $M$. I'm interested in bounding the variance of an unbiased estimator: $$\mathbb{V}\left[\frac1n\sum_{i=1}^nX_i\right]$$...

Question 15

If I have independent and identically distributed random variables $X_1, \dots, X_n$, then are $f(X_1), \dots, f(X_n)$ themselves independent and identically distributed? I think the answer is yes, ...

Stack Exchange Network

Questions tagged [iid]

How to test i.i.d. assumption?

Do i.i.d. assumptions extend to datasets of independently generated sequences in modern sequence models (e.g., RNNs)?

Is Copula Modeling Suitable for Accounting for Temporal Dynamics in Olive Plantation Data?

Variance of product of multiple i.i.d. random variables? [duplicate]

Product of iid random variables contradiction [duplicate]

Expected value of iid squared conditioned on sum

Are $X_i \varepsilon_i$ iid?

Link between Cross-entropy and MLE

Why GLM doesn't have an error term and why shouldn't residuals be i.i.d?

How to understand intuitively the CDF formula for the maximum statistic of three iid rv’s? [duplicate]

Method-of-moment of n IID random variables

Is it possible to describe repeating data patterns as a stochastic process?

Is the Distribution of Survival Times always IID?

Misunderstanding on the use of Popoviciu and von Szokefalvi Nagy's inequalities on the variance of a unbiased estimator

If $X_1, \dots, X_n$ iid, are $f(X_1), \dots, f(X_n)$, also iid? [duplicate]

Hot Network Questions