Questions tagged [definition]

This tag indicates questions about definitions of statistical terms. Use a more general tag [terminology] for questions on statistical parlance that are not specifically about definitions.

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What is the correct definition of the correlation of two random variables?

In the book Signal Processing for Communications by Prandoni and Vetterli, correlation of two variables is defined as the expected value of their product, while the covariance is refered to as the &...
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"observational study vs experiment" why is the answer of the question "experiment " and not "observational study"?

this will be on my exam and i'm indignation to have such confusing/vague questions "validating" my results (explaining me why it is not "confusing/vague" and make me look like a ...
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is the definition of "observational study" wrongly elaboreted?/ observational study vs experiment

Google. "An observational study observes individuals and measures variables of interest but does not attempt to influence the responses" Question that made me have an argument with my ...
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What is the concept of limiting event? [duplicate]

Would any member of Cross validated stack exchange prove highlighted 1 and 2 by simple and clear explanation with examples? My answers: A sequence of events {$E_n, n\geq 1$} is said to be an ...
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Do we really know what does probability mean? [closed]

When I read debates or listen to videos about probabilities and bayesians versus frequentists, it reminds me like a lot the question of "do we know what infinite means?" (related to the ...
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2 votes
1 answer
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What does it mean that the hypothesis space does not contain the target concept?

I read that the algorithm candidate elimination would not converge if the Hypothesis space $H$ does not contain the target concept. You can look it up here. I quoted from the 5th heading: The ...
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Why can the hyperdimensional plane be discribed as $\textbf{w} \cdot \textbf{x} - b$ for support vector machines

So given the picture and the related definitions from this answer: How does the equation $\textbf{w} \cdot \textbf{x}^{(i)} - b = -1$ hold for several vectors $\textbf{x}^{(i)}$ when $\textbf{w} \...
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There are many different quantile definitions - what diffrentiates and motivates them?

First some standard notation. A probability triplet is $(\Omega,\mathcal F, P)$. You have a random variable $X : \Omega \to \mathbb{R}$ measurable function. The distribution function is $F(x) = P(X\...
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Why do we call an assignment mechanism unconfounded assignment mechanism?

Consider some experiment with $n$ units along outcomes $Y=(Y_1,\dots, Y_n)$, covariates $X=(X_1,\dots, X_n)$ and treatment vector $W=(W_1,\dots, W_n)$ where $Y_i=(Y_i^1,Y_i^0)$ for treatment and ...
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What is the difference between a census and a parameter in statistics?

I'm going through my class textbook and the definition for a census is When desired information is available for all objects in the population, we have what is called a census. I remember from ...
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Are there classifiers with infinite number of classes?

I am writing something about time series classification and wrote the following: A classifier is a function that for given input $x_1, ..., x_n$ (in this case representing data stored in audio file) ...
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Can weak-learner be defined in the case of regression problem?

weak-learner is often defined relating to PAC learning. However, to the extent I know, I have never seen the definition of weak-learner when regression. That is, the definition of weak-learner on ...
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Bayesian definition of sufficient statistics

Some time ago I wrote a question about what I think/thought (up to my understanding) is an ambiguity of the common definition of sufficient statistics : Conditioning in the definition of sufficient ...
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What is "natural" about the natural parameterization of an exponential family and the natural parameter space?

In Section 3.4 of Casella and Berger's Statistical Inference, an exponential family is defined to be a set of pdfs or pmfs such that for each member $f(x | \boldsymbol{\theta})$ of the set, $$ f(x | \...
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What is a formal definition of the unique values in an array?

Let the term unique be defined as all other values of this object are numerically different from one value of this object. Let $v$ be a vector with 5000 observations with each observation may or may ...
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Definition of partial correlation

Here (page 415) https://www.stat.cmu.edu/~larry/=sml/DAGs.pdf I found this definition: which confuses me. I am used to see $E[*|Z]$ as a ($Z$-measurable) random variable and as far as I know the ...
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What does it mean for a statistical test to be "robust"?

Is there an intuitive way of understanding what these two sentences mean and why they're true?: "ANOVA is 'robust' to deviations from normality with large samples", and... "ANOVA is '...
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What is the difference between a realisation of a random variable and random variable itself?

I am having a hard time distinguishing random variables from their realisations. (Please note that for the sake of simplicity of my question I use discrete values in my example below.) Usually, a ...
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What precisely is "indeterminacy" in neutrosophic statistics?

In Smarandache 2014, Florentin introduces neutrosophic statistics but I don't get a core part of it. He says: We emphasize, as in neutrosophic probability, that indeterminacy is different from ...
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Federated Learning and Continual Learning: Non-IID Learning

I have some exposure to federated learning and continual learning which are non-iid learning instances [1] and [2] I was wondering can we state the following: Federated learning is when the dataset ...
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6 votes
1 answer
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Statistical significance or Hypothesis testing? [duplicate]

Some seem to insist that Statistical Significance and Hypothesis Testing are different concepts$^\dagger$. Maybe some of them could come forward and explain why they think this way? I came across an ...
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Why does linearly interpolating the quantile work?

I am working on the following exercise: In the lecture we required a quantile $Q_p$ to suffice the condition $$F_n(Q_p^{-}) \le p \le F_n(Q_p) \tag 1,$$ where $F_n$ is the empirical distribution ...
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Time-series correlation if t is negatively correlated with t+1, t+2... but t+1, t+2... are positively correlated

What kind of time-series correlation are we talking about if t is negatively correlated with t+1, t+2, t+3,... but t+1, t+2, t+3,... are positively correlated? So for example, a positive value in t ...
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Definition of Corrected Contingency Coefficient

I quote RACHEV, HÖCHSTÖTTER, FABOZZI, FOCARDI (2010). Starting from the bivariate variable $(x,y)$, with the component variable $x$ taking values in $(v_i, i=1,\dots,r)$ and the component variable $y$ ...
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3 votes
3 answers
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Doubt around Covariance definition

Given the general definition of Covariance between two random variables $x$ and $y$: \begin{equation*} \text{Cov}(x,y)=\frac{1}{n}\sum_{i=1}^n(x_i-\bar{x})(y_i-\bar{y}) \end{equation*} Does the above ...
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1 vote
1 answer
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Data appear in both dependent and independent variable: what is this error called?

I want to find a proper name for the analytical problem I've identified below. One of the most accurate measure of firearm availability is the proportion of suicides committed with firearms, or FS/S (...
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1 answer
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"Relative" Vaccine Efficacy

Merck just released data on their covid-$19$ antiviral medication. In the medicated group there were $28$ unfavorable outcomes in $385$ cases. Or ~$7$% In the placebo group, $53$ negative outcomes in $...
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3 votes
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Relation between variance, square difference and CLT

NEW EDIT TO CLARIFY THE QUESTION My initial question was about why square difference was used instead of absolute value in the formula of the variance... But I ...
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3 votes
1 answer
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What is an "unbiased forecast"?

Assume we estimate a model from the data $(X, Y)$, with some estimator $W(X, Y)$, which is estimating parameters $\theta$ for the model we chose. Then, we would like to perform a forecast for $Y_h$ ...
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Alternative definition of a sample?

From my little knowledge of statistics, a sample is a subset of a population. Now I am reading a textbook on mathematical statistics. In the introductory section of the chapter on sampling ...
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10 votes
5 answers
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Discrete and Continuous variables. What is the definition?

The definition of a continuous variable in our class seems to be, well, not a definition, as there are exceptions not included in its definition. I am a 4th year math student and find it appalling ...
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Is n-dimensional hypervolume different from n-dimensional state space?

Is there any difference between Hypervolumes (e.g. Blonder et al., 2014; Barros et al., 2016) and state spaces (sensu von Bertalanffy, 1972; e.g. Tett et al., 2013)? If so, what is it? It seems that ...
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When would one need to be able differentiate Var(X)?

Reading Blitzstein and Hwang’s introduction to probability http://probabilitybook.net (really good so far!). On page 172, they discuss why $E[|X-E[X]|$ isn’t used as the definition of variance. They ...
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2 votes
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Is a random walk cointegrated with its own lag?

Can a random walk, or more broadly a unit-root process, be considered cointegrated with its own lag? E.g. if $y_t=y_{t-1}+u_t$ with $u_t\sim$ i.i.d., then $y_t$ is I(1), $x_t:=y_{t-1}$ is I(1) and ...
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2 votes
1 answer
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Is there a name for this in statisitics? [closed]

Edit: Ignore this Most of this doesn't make sense and is beyond edits but its too late to delete. If I make too many edits I could be kicked out of this sub like I was in math stack exchange. I don't ...
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What does "nearly orthogonal" mean for a matrix?

I am currently working on experimental designs. I have read several times (e.g Kuhfeld 2010) that for the main effects to be identified, the design matrix has to be orthogonal or "nearly ...
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What is Keras top-k categorical accuracy? [duplicate]

I am working on human activity recognition. I was reading papers and I came across a few where they used top-k categorical accuracy along with accuracy in performance metrics (in Keras). I cannot find ...
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4 votes
1 answer
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When was a random variable first called a "random variable"? And why is it called as such?

From measure theoretic foundations, it is clear that a random variable is neither random nor a variable. It is a deterministic function developed as follows: Construct probability space: $(\Omega, \...
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3 votes
1 answer
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Sequence of random variables vs random sample

I am studying convergence theorems and consistency for estimators. I am confused on the difference between a sample of random variables and a sequence of random variables. Can someone explain the ...
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Criteria to be called a random variable?

I've read that to call something a random variable, that thing must be the result of a statistical experiment. So it got me thinking in which situations might we have an actual bias? For example, ...
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What is the definition of a domain in machine learning?

I have been recently doing a lot of reading into statistical tests for comparing models and I've been coming across the term "domain" and phrases like "domain specific learning" a ...
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Suitable definition of breakdown point for estimators of bounded statistics (i.e constrained estimation)

Let $\Theta$ be a nonempty compact subset of $\mathbb R^d$. For example, the reader may think of the closed unit-ball $\Theta := \{\theta \in \mathbb R^d \mid \|\theta\|_2 \le 1\}$. Consider an ...
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Intuition about the definition of random variables? [duplicate]

I have been struggling a bit with the definition of random variables, as it seems to me a bit of an amorphous concept connected to quite a few different ideas. The Wikipedia article also didn't clear ...
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7 votes
2 answers
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A formal definition of a "measure of association"

I've been trying to come up with a formal definition for a 'measure of association'. An intuitive definition might be something along the lines of 'a function that tells you about the existence or ...
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Bayesian Prior - a distribution conditioned on a set of measure zero? (Definition of a bayesian statistical model)

I am trying to write down the exact definition of a bayesian statistical model in a similar way as the definition for a statistical model. So far I have the definition: A statistical model is a pair $(...
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Degrees of Freedom $\mathrm{df}$ for Multiple Regression with Standarised Variables

Suppose I run a multiple regression on $p$ predictors with a sample size of $n$. The degrees of freedom of the regression are then $\mathrm{df} = n - p - 1$, with the extra $-1$ coming from the ...
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2 votes
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What's the difference between mixed effects logit model and mixed logit model?

Recently,I'm working on a dataset with binary responses. I come across two models with quite similar names, i.e., mixed-effects logit model and mixed logit model. As far as I know, the mixed-effects ...
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Symbol interpretation in non-constant power law density

I am reading Barabasi book on network science. I am struggling to interpret the density formula for a power-law degree distribution with low-degree saturation and high-degree cut-off (http://...
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Probability distribution over a variable? What does it mean?

In this document http://legacydirs.umiacs.umd.edu/~xyang35/files/understanding-variational-lower.pdf at the very first page, it says: Moreover, uppercase P(X) denotes the probability distribution over ...
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What does "autocorrelation/heteroscedasticity of the errors" mean?

When learning clustering error, from this discussion In general, you should look to cluster-adjust standard errors at the level in which you believe there exists autocorrelation/heteroscedasticity of ...
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