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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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In optimization, what is the purpose of Gateaux and Frechet derivatives?

When reading Optimization related papers, I sometimes come across terms such as "Gateaux" or "Frechet" derivatives. I'm often puzzled as to why we need these definitions, when we already know the ...
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32 views

On the target function in machine learning

I'm beginner to machine learning and start it with Mitchell's book. In page 7 of it he speaks about target function and says that we want to give a number for every board state in checkers game by ...
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1answer
17 views

What is the definition of layer in neural network?

What is the precise definition of layer in neural network? Are things like concatenate functions, activations, batch normalizations, skip connections considered as layers?
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1answer
25 views

Name of functional part of a pdf after removing proportionality constants?

Let $f(x;\theta)$ be probability density function. Suppose that this pdf contains a proportionality constant $c$, so that $f(x;\theta) = c\cdot g(x;\theta)$, where $g$ is an integrable function. Is ...
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1answer
34 views

Frequentist definition of probability and prediction?

The frequentist definition of probability states that: The probability of an event is the ratio of the number of cases favorable to it, to the number of all cases possible when nothing leads us to ...
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1answer
35 views

VC dimension of sine family is infinite?

From what I understand, the VC dimension of an hypothesis class is given by the maximum number of points in general position (or random) on the domain space that can be arbitrarily labeled by the ...
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1answer
74 views

The definitions of estimator and estimate

This example demonstrates the difference between a theoretical observation and a realized observation. A theoretical observation is a random variable with a probability distribution, while its ...
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1answer
32 views

What's the difference between outlier analysis and clustering?

What's the difference between outlier analysis and clustering? When clustering is done isn't that outliers (if exist) are also found? Sorry for this simple question.
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2answers
227 views

Is there a difference between Bayesian and Classical sufficiency?

The title pretty much says it all. I wonder whether there is any difference in the way Bayesians understand sufficiency vs. the way orthodox statistics understands sufficiency, or are they equivalent? ...
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1answer
971 views

Is supervised learning a subset of reinforcement learning?

It seems like the definition of supervised learning is a subset of reinforcement learning, with a particular type of reward function that is based on labelled data (as opposed to other information in ...
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3answers
2k views

Is there more than one “median” formula?

In my work, when individuals refer to the "mean" value of a data set, they're typically referring to the arithmetic mean (i.e. "average", or "expected value"). If I provided the geometric mean, people ...
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41 views

monotonic vs non monotonic models

I am reading this paper and it mentions monotonic and non monotonic functions. I only only what is monotonic and non monotonic function is, I do not really understand it in the scope of their ...
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59 views

Equivalence of sufficient statistics definitions [duplicate]

I'm reading about sufficient statistics, and have come across two definitions which seems unrelated, and I'm trying to understand their connection. The first definition is from Wikipedia A ...
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1answer
113 views

What is the difference between Cronbach's alpha and standardized Cronbach's alpha?

I found in the wiki article a definition of a standardized Cronbach's alpha but nothing is said what it is and about its relation to the original Cronbach's alpha: I found at What is Cronbach's ...
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27 views

Probit model specification

im writing a paper that involves using a probit regression, would this be a correct summary of what a probt model is and how it works?: "the probit specification is a binary-dependent model that ...
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1answer
24 views

Definition of forecasting period in time series

I am new to forecasting time series. The team that I am working with keep referring to forecasting period as lag. For example we have 20 month of data and we would like to create 5 month forecast. Is ...
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1answer
327 views

Size of the Hypothesis Space

(I'm asking the same question as the linked one, I simply don't have enough reputation to comment yet, but hopefully, this one will more clearly explain what me and the other asker both mean) Let's ...
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1answer
262 views

What's the definition of “Dynamic Regression Models”?

I am trying to learn about Dynamic Regression models. However, the sources on the topic is (relatively) few compared to other TS topics, and so I cannot really get a grasp of where to start. I really ...
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3answers
135 views

I need help clarifying the term forecast interval

I am reading Introduction to Time Series Analysis and Forecasting by Douglas Montgomery et al. They describe the term forecast interval as: The forecast interval is the frequency with which new ...
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0answers
16 views

Definition of stable distribution

In some places, I find the following definition of stable distribution: A distribution is said to be stable if a linear combination of two independent random variables with this distribution has ...
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0answers
34 views

Does a time series start at $t=0$?

I am a beginner in Time Series Analysis and I am reading something about the most simple processes like AR and MA. So far I understood that one wants to have the following result: The MA($\infty$)-...
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1answer
82 views

Alternate (?) definition of sample variance [duplicate]

The variance of a sample can be defined as $$s^2 = \frac{1}{2}\frac{1}{n(n-1)}\sum_{i}\sum_{j\ne i}\left(x_i - x_j\right)^2$$ Apart from the factor of $1/2$, this can be paraphrased verbally as ...
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3answers
355 views

What is the precise definition of unsupervised learning?

Let's look at a special case: Generative Adversarial Networks (GANs). (For those who don't know what a GAN is: for this purpose they are two neural networks that are trained using user generated ...
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0answers
42 views

question about correct interpretation of sufficiency

I am currently trying to understand the concept of sufficiency and I am trying to create my own example. Assume that we have a statistic$$T:(\mathscr X, \mathscr A, \mathscr P) \to (\mathbb{R}^2, B^2)...
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1answer
91 views

What does linear time series refer to?

In some papers or documents, "linear times series" seems to refer to a time series that can be modeled as a linear AR (auto-regressive) model. In other places, "linear time series" seems to refer to ...
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2answers
205 views

What is a probability distribution? [duplicate]

This is a very basic question, and maybe a silly one, but I'm struggling to understand the actual definition of a probability distribution. In Wasserman's "All of Statistics", for example, he says ...
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1answer
1k views
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120 views

“Pragmatic” trials: what are they?

On twitter, a trialist Stuart Nicholls critiqued a recently published study by saying: Further to the very interesting paper by Dal-Re they flag several examples that question usage of the term ...
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1answer
31 views

Unsure about result given in lecture

I'm looking through my notes and something my lecture said seems off, just want to clarify. "Let $Z_1,\ldots, Z_n$ be iid N(0,1) random variables and let $\overline{Z}$ be their average. Then $\...
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Is it a problem that limiting frequencies (can) violate countable additivity?

I`ve stumbled upon the following paper by Alán Hajek https://www.jstor.org/stable/40267419, in which the author states that the Frequentist interpretation of probabilities as limiting frequencies ...
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1answer
126 views

What is variable importance?

Searching this site, I see over 1,000 posts triggered by the search term "variable importance", mostly machine learning related. However, I've never encountered the definition before. Is it a term ...
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0answers
39 views

Is the $t$-test asymptotically nonparametric?

Wikpedia defines "parametric statistics" as: ...a branch of statistics which assumes that sample data comes from a population that follows a probability distribution based on a fixed set of ...
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110 views

Do random variables follow the same algebraic rules as ordinary numbers?

In the comments on my answer to a recent question about the sum of random variables, I came across a link to the Wikipedia article on the ratio distribution, and noticed the following peculiar claim ...
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2answers
42 views

Is bounds of parameter hyperparameter?

Suppose I set [Smin, Smax] to be the limits of slope of a regression, are they hyperparameter? If not, what are they called?
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1answer
61 views

Defining Diversity in Ensemble Learning

I have a few questions regarding on how diversity is defined since I've seen differing definitions in different papers. In the paper "Measures of Diversity in Classifier Ensembles and their ...
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0answers
35 views

What is Exact definition of Invariance principle

Books wrote a lot about invariance definition and method to obtain invariance estimators, tests, and etc. However I couldn't find exactly the definition of principle of invariance. Is there any good ...
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0answers
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Definition of moments and the different approaches to compute them [duplicate]

I was wondering about the way we refer to the term "moments". In statistics and probability the first moments is the mean $$E[X^1] $$ The second moments is the variance: $$E[(X-E[X])^2]$$ I notice ...
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1answer
516 views

What exactly does “wald test” mean?

I am reading possibly conflicting statements in different sources. Sometimes I think I understand that the word "Wald test" refers to any kind of test of whether the value of a parameter (whether ...
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3answers
764 views

Is the linearity assumption in linear regression merely a definition of $\epsilon$?

I am revising linear regression. The textbook by Greene states: Now, of course there will be other assumptions on the linear regression model, such as $E(\epsilon|X)=0$. This assumption ...
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0answers
34 views

Learning Tasks that do Satisfy Realizability Assumption

I am trying to read Understanding Machine Learning by Schwartz and David. I just am trying to understand realizability assumption. According to the textbook, the realizability assumption means you can ...
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14 views

Is sufficiency “conditional ancillarity”?

Question: Would it be correct to say that a statistic $T(X)$ is sufficient w.r.t. the model $\mathcal{P}$ if and only if the data $X$ is an ancillary statistic with respect to the "conditional model" $...
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111 views

How to add and multiply distributions?

I saw in a statistics book a problem. Let $X$ be a distribution that gets $1$ for probability $0.4$ and $2$ for probability $0.6$. Compute the mean and variances of $Y=3X-2$ and $Y=3X^2-2$. I found ...
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3answers
184 views

Is the posterior distribution $P(\theta|\mathbf{X})$ a statistic?

The textbook definition of a statistic is any function of the data, $g(\mathbf{X})$. Much of frequentist inference is concerned with deriving sampling distributions for various statistics under some ...
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130 views

Linear regression model identifiable?

I understand the concept of identifiability in the context of distributions. This is $f$ is identifiable if $f(x;\theta) = f(x;\theta')$ for all $x$, if and only if $\theta=\theta'$. However, in the ...
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2answers
4k views

What is a strict definition of U-shaped relationship?

I now have seen several papers that analyze U-shaped or inverse U-shaped relations among variables (in a regression framework). The general understanding I have from there is that it is a specific ...
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0answers
35 views

Are credible intervals confidence regions? [duplicate]

I understand that I'm asking a very pedantic question, but as far as I'm aware a confidence region is a multi-dimensional generalization of a confidence interval and therefore as a credible interval ...
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0answers
183 views

Estimator that is optimal under all sensible loss (evaluation) functions

Consider a probability distribution $D$ with a parameter $\theta$ and an i.i.d. sample $S$ from that distribution. I am interested in an estimator $\hat\theta(S)$ of $\theta$ that satisfties the ...
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1answer
48 views

Why must a random variable be $\mathcal{F}$-measurable?

Needless to say, I know that the answer is trivially "because that's part of the definition of a random variable", but what I'm really looking for is why that's part of the definition. Why do we want ...
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1answer
8 views

Does combining two standardized test results to a standardized test?

Let's say I have two standardized tests, test A and test B. If I combine the two tests (no items will be discarded, all will be included) to make test C. Can we say test C will be also a standardized ...
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1answer
123 views

What is statistic in statistics?

I am getting difficulty in understanding the definition of the statistic. From wikipedia, I come to understand that statistic is any 'information'(range, mean, variance) of any sample of any given ...