Questions tagged [example]

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Is there a statistic such that for large sample sizes $a_n (\hat{\theta} - \theta) \sim N(0, \Sigma)$ approximately but $a_n \neq n^{1/2}$?

Various central limit theorems are of the form $a_n(\hat{\theta}-\theta)\sim N(0, \Sigma)$ approximately as $n \to \infty$ and usually $a_n = n^{1/2}$. Are there central limit theorems for statistics ...
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What is a good introductory guide to Bayesian MCMC Analysis in R?

I am trying to perform Bayesian Analysis in R, using of Monte Carlo Markov Chains to calculate the probability of, in a set of data, there being a gaussian peak at a certain location $x_0$ (my 'target'...
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1 answer
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Accuracy failure example

I am trying to understand the functioning of accuracy and I need a practical example. This is what I understood: it gets the average correctness of the predictions and in some cases its result can be ...
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Computing an Exponential Moving Average

According to the Wikipedia page on moving averages, "This is also why sometimes an EMA is referred to as an $N$-day EMA. Despite the name suggesting there are $N$ periods, the terminology only ...
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Example of a parametric family of distributions that always has dependence on among its variables

Inspired by this question, I would like an example of a parametric family of distributions such that there is dependence for all choices of parameters. The family could be infinite or finite, but I ...
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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 \...
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Downward slope but Spearman correlation coefficient is positive and vice versa

Why the slope and the Rho value not the same? For examples, graph H-DSI shows downward slope but the Rho value is positive (P value=0.9603; r=0.009867). Hope someone can explain it. Thank you. H DSI ...
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Choice of covariance matrices in Kalman filtering?

I am attempting to learn about Kalman filtering. I understand the state vector, call it $\mathbb{x}$, comes with a covariance matrix call it $P$. I can initially choose my $\mathbb{x}$ by my pre-...
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8 votes
1 answer
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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 ...
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Examples of correlated Xs with opposite effect on Y [duplicate]

Could someone give me a simple real life example of how two things can be positively correlated, but they have different (opposite) effects on a third variable? I encountered this scenario and I'm ...
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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 ...
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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 ...
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3 answers
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Real-life example in which Markov chain Monte Carlo is desirable? [duplicate]

A typical introduction to the Metropolis--Hastings algorithm, and hence to Markov chain Monte Carlo techniques in general, starts with the following assumptions on some probability distribution $P(x)$ ...
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Kwiatkowski–Phillips–Schmidt–Shin (KPSS) and Augmented Dickey–Fuller (ADF) Tests

I have been searching for a sample usage of the KPSS and ADF tests, however I can only find pages reporting examples using R or Python. The mathematical definition of the KPSS test also seems to be ...
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How to use missForest in R for test data imputation?

I want to use the R missForest() function at work to perform missing value imputation. However, after reading up on the algorithm more, I can't decide how to impute ...
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6 votes
2 answers
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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 ...
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2 votes
1 answer
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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 ...
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1 vote
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Am I understanding correctly the Maximum Entropy concept using a sentence?

In the sentence "The house is white", each word carries a different amount of information. If I remove the "The" from the sentence, almost nothing happens: you are still able to ...
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3 votes
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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 ...
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1 answer
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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 ...
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1 answer
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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 ...
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1 vote
1 answer
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Example of random process with negative variation

I study about random processes. Let us have $\{X_1, X_2, \dots X_n\}$ observations. I learned, that in stationary time series the sample autocovariance function is defined as $$ \widehat{γ}(h)= \...
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Instructive example for using machine learning to predict continuous variable?

Arguably, the MNIST or titanic examples are probably the most common and instructive examples of classification problems solved using machine learning. Are there any 'iconic' examples of machine ...
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What scenario corresponds to choosing the "true distribution" $p$ in $\textsf{KL}(p\parallel q)$?

I understand that when you think about changing $q$ in the Kullback-Leibler divergence $\textsf{KL}(p\parallel q)$, this corresponds to trying to find the distribution that minimizes information loss ...
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What are 3 easy, real-world examples for high, medium and low correlation?

I understand what correlation means on paper (as in: given high, positive correlation, then, if A is high, B is likely to be high, too). However, the classification into "high", "medium" and "low" ...
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1 answer
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Example of a Markov Process with observable states?

I have a pretty good handle on Hidden Markov Models, but I can't think of any examples of a Markov process with a directly observable state. Any examples?
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5 votes
2 answers
156 views

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 ...
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1 answer
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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 ...
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1 answer
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where can I find advanced stats questions and answers like the example below?

I am at the beginning of an advanced stats course and I am looking to practice some questions beyond the few which are given in class. below are a few examples from our first assignment. I am looking ...
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How to use parameters to calculate a value which will be used for a statistical analysis?

I am confused on a basic statistics concept. Also, my terminology may be a bit off as well; I am a novice. I will be as simple and concise as possible. Hopefully, this scenario gets to the core of my ...
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1 vote
1 answer
2k views

Power function of a test,example

Consider a population with the pdf $N(\theta,1)$ where $\theta$ is unknown and hypothesis $H_0:\theta=5.5$ and $H_1:\theta=8$.Suppose that $\bar{X}=\frac{1}{9}\sum_{i=1}^9 X_i.$Reject $H_0$ iff $\bar{...
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3 votes
3 answers
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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 ...
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1 answer
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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 ...
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1 vote
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What is the probability of Jack finding Sam at the last bar?

Jack and Sam are friends. It is Saturday and Sam forgot his phone home. Jack knows that there is a 2/3 probability that Sam goes to a party. There are 10 clubs in town and all have an equal ...
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2 votes
2 answers
5k views

Smarter example of biased but consistent estimator?

I am trying to get an intuitive understanding of why there exists biased but consistent estimator. Suppose $X_i \sim \mathcal{N}(\mu, 1)$. One example I came across is this: $$W_n(X_1,\cdots,X_n) = ...
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2 votes
1 answer
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Regression example for one-dimensional input

For some educational purposes, I need a realistic regression example where the input space is one-dimensional, i.e. $x\in\mathbb{R}$. I do not want to use any dummy approaches such as simulation from ...
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1 vote
1 answer
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Difference between instance-based and example-based Learning

I've read both the terms instance-based and example-based learning in some contexts, e. g. instance-based learning for label ranking and example-based for general text classification tasks. Is there ...
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6 votes
1 answer
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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 ...
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Real world practical Outliers/Anomalies

I want to have some real life and practical examples for anomalies that can be expressed like a scenario. For example in a country following left-hand driving, a vehicle moving in a wrong direction ...
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What are the first historical examples of meta-analysis?

I am researching the history of meta-analysis, and have found several interesting scholarly sources, going O'Rourke to Hedges, just to name two recent ones. On top of these authoritative sources, I ...
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9 votes
1 answer
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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. ...
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