Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [example]

38 questions
9
votes
1 answer

Example of a stochastic process that is 1st and 2nd order stationary, but not strictly stationary (Round 2)

This question follows from my previous question, where Robin answered the question in the case of weak stationary processes. Here, I am asking a similar question for (strong?) stationary processes. I'll define what this means (the definition can…
Robby McKilliam
  • 2,010
  • 14
  • 14
8
votes
1 answer

Is there a real example in which a correlation finally leads to the discovery of a non-trivial causal relationship?

More specifically, I am wondering if there is such an example satisfying the following criteria: The example happened after 1888, it would be better to be after 1900—I think few people have the conception of correlation before Galton's 1888…
Eli4ph
  • 181
  • 3
8
votes
1 answer

Model with admissible estimator(s) that are not the Bayes estimator for any choice of prior?

Every Bayes estimator is admissible, to the best of my knowledge. (Related questions - 1,2.) I recall my professor mentioning once during a lecture that, at least as rough intuition, the converse is true as well, that is, every admissible estimator…
Chill2Macht
  • 5,639
  • 4
  • 25
  • 51
6
votes
2 answers

On the difference between the main effect in a one-factor and a two-factor regression

Consider a linear regression (based on least squares) on two predictors including an interaction term: $$Y=(b_0+b_1X_1)+(b_2+b_3X_1)X_2$$ $b_2$ here corresponds to the conditional effect of $X_2$ when $X_1=0$. A common mistake is to understand…
Arnaud Mortier
  • 604
  • 3
  • 13
5
votes
2 answers

Teaching (very elementary) statistical modelling

I've been asked to contribute some lectures (or parts of lectures) to a course on "Mathematical Modelling", from a statistical perspective. This is to a rather mixed group of Mathematics undergraduates: some may have only seen one course on…
Matthew Daws
  • 131
  • 7
5
votes
1 answer

Negative autocorrelation in linear regressions : examples and consequences

I am wondering if there are classical (or not so classical) examples of negative autocorrelation in a regression model. To expalin the context : I am explaining OLS limitations, heterosckedasticity and autocorrelation for the moment, and I want to…
Anthony Martin
  • 1,109
  • 3
  • 11
  • 26
4
votes
2 answers

Symmetric distribution with finite Mean but no Variance

Is there a symmetric continuous distribution that has a finite mean, but no variance? What I've found so far: For instance the Pareto distribution satisfies everything but the symmetry, so I was wondering, can we also construct a symmetric…
flawr
  • 563
  • 4
  • 15
3
votes
0 answers

Examples of positive definite periodic covariance matrices

My aim is to find a few examples of positive definite covariance matrices $\pmb{R} = \{R(s,t)\}_{s,t=1}^n$ that satisfy $$R(s,t) = R(s+T, t+T),~~~1\leq s,t \leq n-T,$$ where $T$, $1\leq T\leq n-1$, is a fixed positive integer. I have tried to…
Joy
  • 313
  • 1
  • 16
3
votes
3 answers

Under torture, the data may yield false confessions. Examples?

My statistics teacher repeated the statement "Under torture, the data may yield false confessions" several times, but without giving a concrete example of what it means. Can you give some good examples that show the aim of the statement?
Nisba
  • 131
  • 6
2
votes
2 answers

A realistic example of a non identifiable model?

Given the definition of statistical model identifiability : identifiable iff $P_\theta = P_{\theta'} \implies \theta = \theta' ~~ \forall \theta, \theta' \in \Theta$ we can see that, for example, $X \sim N(\frac{\theta_1}{\theta_2},1)$ would not be…
Antonello
  • 191
  • 7
2
votes
1 answer

concrete example of degenracy

I was reading on degeneracy. Can someone give concrete example of following definition. A kernel $h$ is symmetric if it is invariant under permutations of its inputs. $S_m$ be symmetric group containing all permutations of $m$ elements. For any …
manifold
  • 33
  • 8
2
votes
1 answer

Statistics/Data Science: Real world example for a donut destribution?

I'm looking for different real world examples for donut distribution (in the statistic meaning). https://i.stack.imgur.com/VrGq4.jpg For the most other distributions, I found good examples. But for this the only one is the way to focus a laser…
Clemens Drolshagen
  • 23
  • 3
2
votes
1 answer

Question about latent variables in Co-integration Regression

I have a question about cointegration regression models as follows: Is it common to have latent variables or regressors with measurement error in the cointegrating regression model? Is it highly motivated? Please provide some examples. Much…
Sarah
  • 103
  • 1
  • 8
2
votes
1 answer

Two random variables not correlated with normal distribution, whose sum is normal but which are not independent

The example based on the Rademacher distribution of two random variables, $X$ and $Y$, normally standard distributed, not correlated, but not independent, is well known. Additionally, in this example it is shown that $X$ and $Y$ are not jointly…
G al Cubo
  • 23
  • 4
2
votes
1 answer

Numerical Example of Independent Component Analysis

Can somebody explain ICA(Independently Component Analysis) with a small practical example over here. I have seen lot of programs and libraries written and you can just apply that to your data to find ICA components. One such library is famous python…
Naseer
  • 365
  • 1
  • 3
  • 16
1
2 3