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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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1answer
19 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
28 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
53 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
50 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
12 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
33 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($\infty$)-...
8
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1answer
73 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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4answers
254 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
41 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
39 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 ...
8
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2answers
189 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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3answers
105 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
29 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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0answers
53 views

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
58 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 ...
2
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0answers
32 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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0answers
106 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
39 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
53 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
31 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
18 views

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 ...
0
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1answer
379 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 ...
8
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3answers
340 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
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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87 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
155 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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0answers
107 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
2k 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
33 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
178 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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0answers
29 views

What arguments of a kernel OR covariance function called?

Any kernel ${\displaystyle K(\mathbf {x} ,\mathbf {x'} )}$ take two arguments $\bf{x}$ and $\bf{x}'$ and provides a measure of closeness. The arguments could either be scalar or a vectors. I would ...
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0answers
27 views

Does the Wiener process require $W(t_0)$ to be independent of all increments?

I've been going through some lecture notes and I've found said condition as part of the definition of the Wiener process. As far as I'm aware this is a non-standard definition (and may even be an ...
2
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1answer
46 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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33 views

Definition Copula Analysis

What are the difference between empirical copula, theoretical copula and parametric copula. I need a simple explanation because i cannot differentiate between them.
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1answer
7 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 ...
3
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1answer
113 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 ...
0
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1answer
13 views

Can we give posttest without having pretest?

The Merriam-Webster Dictionary defined posttest as a test often used in conjunction with a pretest. The dictionary used "often", so can we give posttest without having a pretest? https://www.merriam-...
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0answers
92 views

What is the difference between concept class and hypothesis

Formal definition that I have seen of concept class is class of all true functions mathematically : f:X→{0,1}f:X→{0,1} and that of hypothesis is: h:X→{0,1}h:X→{0,1} But most of the times ...
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0answers
23 views

Origin of “machine” in SVM, GBM etc [duplicate]

Is it known who originally introduced the term "machine" used in terms like machine learning, support vector machine or gradient boosting machine? Could it be defined as an "algorithm that fits a ...
0
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1answer
64 views

Perceptron definition doubts

I'm preparing a presentation about neural networks and I have doubts about the perceptron definition. Some sources I found in the internet tell that it's a basic artificial neuron, thus it's the basic ...
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0answers
21 views

(When not assuming differentiability) what is the definition of Fisher information?

Here we assume (for simplicity) that the parameter $\theta$ is one-dimensional. When one has sufficient regularity and can push in partial derivatives to and pull out partial derivatives from the ...
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70 views

What is a fourth-order stationary process?

What is a $n$th-order stationary process, where $n >2$?
2
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1answer
122 views

Definition of Overfitting

Consider error of hypothesis h over training data errortrain(h) and error over entire distribution D of data errorD(h). Hypothesis h in H overfits training data if there exists an alternative ...
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0answers
12 views

What is a time-series signal? [duplicate]

Let's assume we have a CNC machine cutting an aluminium block and we are monitoring its RMS power consumption at a constant sample rate e.g. 1Hz (see figure below for example). Can this considered to ...
0
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1answer
24 views

Perceptron algorithm - is this a typo or did something change in this equation?

I'm currently reading Python Machine Learning (Amazon link) by Sebastian Raschka. Here discussing Frank Rosenblatt's perceptron algorithm: More formally, we can pose this problem as a binary ...
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3answers
967 views

Is machine learning an heuristic method?

I'm asking this out of curiosity. In the past I have thought of an heuristic as a "quick and dirty" rule not based on data analysis, as opposed to a solution which uses machine learning or ...
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1answer
98 views

What is the definition of probability on a continuous distribution?

If I have a continuous distribution, $N$. I say $f$ is a sample from $N$, $f \sim N$. Now I want to determine the probability of $f$ having a value of $x$: $$ P(x)=\lim_{t\rightarrow0} {\frac{\text{...
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0answers
64 views

First, second and third-order bias

I came across first, second and third-order mean bias of an estimator in a text and I could not find a good reference which explains them properly. Can somebody please explain these terms to me or ...
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0answers
106 views

Is a random walk necessarily a martingale?

I read in the following notes (http://www2.econ.iastate.edu/classes/econ672/Falk/_notes/lecture_4_martingales.pdf, p.2) that "a random walk is a martingale." Although it seems logical with the used ...
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1answer
2k views

What's the difference between binary and binomial data?

I read terms binary data and binomial data in a textbook. What's the difference between them?