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 definition of a non-linear estimator? I heard that ratio of estimators is non-linear

Why don't we consider nonlinear estimators for the parameters of linear regression models? says that LASSO is a non-linear estimator. I think LASSO has a solution via matrix multiplication. I don'...
5 votes
2 answers
2k views

When is a statistic not a statistic?

I have a fairly involved ``statistic'' that involves transformation of a set of samples $\mathbf{x}$ by a massive machine-learned matrix and subsequent nonlinear processing into said statistic $\...
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1 answer
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Define plateau of sigmoid function

I have a sigmoid function ...
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Definition of correlation between events?

I often hear people talk about correlation between events, e.g. event A and event B are positively correlated. However, unlike correlation between random variables (i.e. $\frac{Cov(X,Y)}{\sigma_X \...
1 vote
0 answers
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Does the tetrachoric/polychoric covariance and variance exist?: Does a "pseudo" correlation exist? [closed]

Does the tetrachoric/polychoric covariance and variance, and mean exist? If not, I think the tetrachoric correlation is a pseudo-correlation, and akin to Kl-divergence is not a distance metric.
1 vote
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How to express in mathematics "standarized residuals pre-multiplied by the inverse square-root factor of the estimated error correlation matrix"?

What is the explicit formula for "standarized residuals pre-multiplied by the inverse square-root factor of the estimated error correlation matrix"? Suppose x is a fitted object of type lm, ...
2 votes
2 answers
83 views

A Rigorous Definition of Data Generating Process (DGP)

I am trying to find a rigorous mathematical definition of a data generating process (DGP) under a well-defined probability space. The closest source I have found on Cross Validated is this one, and it ...
2 votes
1 answer
131 views

What does 'Parent Distribution' mean in statistics?

I am studying some articles related to statistics and some of them mention the term 'Parent Distribution'. What does that mean? Is it a distribution model that the authors decide to use as a basis of ...
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What is effect size?

It might be silly question-want to have clarity of this concept.I was wondering if someone can elaborate meaning and examples of effect size in clinical research. How to interpret it accurately? How ...
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1 answer
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Can a consensus be reached on the exact meaning of "Cohen's D" and "Hedge's G"?

This question: Difference between Cohen's d and Hedges' g for effect size metrics shows there are at least two different interpretations each of both Cohen’s D and Hedge’s G, one of them in ...
1 vote
0 answers
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Loss function definiton for relabelling

Taken from the appendix to the paper (Yongning Wang & Ruey S. Tsay) of this (2019) paper Clustering Multiple Time Series with Structural Breaks. Appendix to be downloaded her Appendix To fix label ...
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1 answer
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What does it mean to say that a covariance matrix is ​a positive definite matrix? [duplicate]

I'm doing a work on covariance matrix and this question came to me that was not very clear.
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Is the probability attached to a random variable inherited from the outcomes, or is it simply the CDF of the mapped points? [duplicate]

This is self-study. I realized I had not payed attention to the definition of a random variable, and it is different than I thought. I understand a random variable (RV) maps from outcomes (or events?) ...
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Does the term Big Data refer to large number of features or datasize-per-feature? [duplicate]

I understand that Big Data means a dataset with a large number of feature values whether or not it has an enormous size of data in each feature. Is my understanding correct, or is it the other way ...
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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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1 answer
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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 ...
1 vote
0 answers
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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 ...
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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0 answers
25 views

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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0 answers
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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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1 vote
1 answer
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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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1 answer
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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 ...
5 votes
3 answers
251 views

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) ...
2 votes
2 answers
88 views

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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3 votes
1 answer
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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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4 votes
2 answers
225 views

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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2 votes
1 answer
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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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14 votes
3 answers
2k views

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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2 votes
2 answers
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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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2 votes
1 answer
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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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1 vote
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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 ...
6 votes
1 answer
106 views

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 ...
0 votes
0 answers
35 views

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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2 votes
1 answer
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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 $y$ ...
3 votes
3 answers
559 views

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 ...
1 vote
1 answer
51 views

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 (...
0 votes
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 $...
3 votes
0 answers
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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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1 vote
0 answers
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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 ...
10 votes
5 answers
2k views

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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1 answer
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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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2 votes
0 answers
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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 ...
2 votes
0 answers
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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 ...
2 votes
1 answer
143 views

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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2 votes
0 answers
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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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