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
18 views

Obvious counter examle to the Handshaking Lemma [on hold]

The Handshaking Lemma is described thusly in Wikipedia: In graph theory, a branch of mathematics, the handshaking lemma is the statement that every finite undirected graph has an even number of ...
1
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1answer
18 views

Is there a difference between on-line learning, incremental learning and sequential learning?

What I mean is the following: Instead of processing all the training data at once and calculating a model or hypothesis, we process one data point at a time and update the model directly afterwards. ...
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0answers
15 views

What, if any, is the precise definition of “substantively large”?

I am told that while my estimates are not statistically significant, they are "substantively large". Is there a precise definition for the phrase "substantively large"? If I say that my estimates ...
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0answers
18 views

Homoscedasticity - constant second moment or constant variance

I found the following different definitions of homoscedasticity and I'm wondering which is the correct one. The second moment is constant, i.e. E(X²)=s² (see e.g. p.11 ...
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1answer
31 views

Reference for definition of multiple-output Gaussian process

Does anyone know any good reference that has a clear and precise definition of multiple-output Gaussian process? Something like the definition of the Gaussian process in the third page of this set of ...
1
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1answer
32 views

What is a random variable in the definition of a linear regression model

In wikipedia's definition of a linear regression model: $y_i = \beta_1 x_{i1} + \cdots + \beta_p x_{ip} + \varepsilon_i = \mathbf{x}^{\rm T}_i\boldsymbol\beta + \varepsilon_i, \qquad i = 1, \ldots, ...
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2answers
80 views

What is a Highest Density Region (HDR)?

In statistical inference, problem 9.6b, a "Highest Density Region (HDR)" is mentioned. However, I didn't find the definition of this term in the book. One similar term is the Highest Posterior ...
4
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2answers
170 views

What is a multivariate random variable?

I've been trying to read the Wikipedia article on multivariate random variables but I'm having trouble getting past the math. Is there a more intuitive explanation? I'm assuming that a univariate ...
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1answer
88 views

Can you reduce the risk involved in an uncertain event?

I'm not sure if this is the right Stack Exchange site but I felt it came closest. Based on Knights 1971 definition of risk uncertainty is defined as a situation where factors exogenous to the ...
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1answer
54 views

Autocorrelation definition

I am formatting a statistics proof, and I wanted to make sure that I have the definition of autocorrelation correct. Is it the case that the autocorrelation of a continuous variable is the same as ...
11
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3answers
288 views

What exactly is a distribution?

Sorry for such a basic question. I know very little of Probability and Statistics, and am wishing to learn. I see the word "distribution" used all over the place in different contexts. For example, ...
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0answers
30 views

Why are observations from a random variable considered as random sample?

In a couple of books I've read a random sample is defined as a set of $n$ independent identically distributed random variables. And then their behavior is developed based on this definition which I ...
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0answers
23 views

The most general definition of the Likelihood function for continuous data (including truncation and censoring)

How would you rigorously define the likelihood function for censored/truncated observations? Even in most lifetime/reliability literature (where these types of observations are frequently encountered) ...
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0answers
36 views

Rigorous definitions of sample and population

I am trying to understand some basic ideas of econometrics (and mathematical statistics) from the precise, mathematical point of view, avoiding vague explanations. I am beginning to learn about these ...
2
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1answer
121 views

Two different definitions of a median

I read from the book "Introduction to the Practice of Statistics", The International Seventh Edition, page 31 that "The $\textbf{median $M$}$ is the midpoint of a distribution. Half the observations ...
2
votes
2answers
113 views

In the definition of probability density function, does it matter if the interval is open or closed?

I can find two definitions of Probability Density Functions in the sources I have checked: $$P(a < X < b) = \int^b_a f(x)dx$$ Ref: Hogg & Tanis, Probability and Statistical Inference and ...
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2answers
94 views

Why is the standard deviation defined using differences^2 instead of differences^4? [duplicate]

I've read some post about why to take the std. deviation and its benefits, here's one of them: Why square the difference instead of taking the absolute value in standard deviation?, and another by ...
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0answers
38 views

What is industrial statistics?

We have a course titled "Industrial Statistics". But I don't understand what is industrial statistics? What I have understood after searching some sites is only that Industrial statistics ...
0
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1answer
27 views

What is intervention?

An intervention is strategy to produce change among individuals or entire population. Is the definition of intervention correct ?
4
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1answer
52 views

Is there a basic definition of Significant result and Non-significant result?

Is there a basic or widely accepted definition of Significant Result and Non-Significant Result? Seems that every where I look they want to get into problem solving without defining what those terms ...
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0answers
42 views

Is a model including a square root of a variable linear in the parameters? [duplicate]

Is the model $$ y = \gamma_0 + \gamma_1 + \sqrt x + \varepsilon $$ linear in parameters? ( $\varepsilon$ is the error term.)
3
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0answers
27 views

How to construct “reference priors”?

I have been reading about noninformative priors. Two of the most popular priors of this kind seem to be the Jeffreys prior and the reference prior. The Jeffreys prior has a clear construction, being ...
5
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2answers
51 views

Short term for Probability of Type I error

When comparing statistical tests, one often compares the probability of committing a Type 1 error, and the probability of not committing a Type 2 error. While (2) can be concisely termed 'power', ...
5
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3answers
133 views

What makes constant function an estimator?

This is a theoretical one. This question is inspired by recent question and discussion on bootstrap, where a constant estimator, i.e. a constant function $$f(x) = \lambda$$ was used as an example of ...
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1answer
24 views

What does it mean to say that two classifiers are independent?

For example: http://www.tandfonline.com/doi/abs/10.1080/00031305.2013.778788 Is it simply that neither classifier uses the output of the other?
6
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2answers
139 views

Is a time series the same as a stochastic process?

A stochastic process is a process that evolves over time, so is it really a fancier way of saying "time series"?
9
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1answer
589 views

How does “Fundamental Theorem of Factor Analysis” apply to PCA, or how are PCA loadings defined?

I'm currently going through a slide set I have for "factor analysis" (PCA as far as I can tell). In it, the "fundamental theorem of factor analysis" is derived which claims that the correlation ...
9
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4answers
297 views

What is the difference between $E(X|Y)$ and $E(X|Y=y)$?

Generally, What is difference between $E(X|Y)$ and $E(X|Y=y)$? Former is function of $y$ and latter is function of $x$? It's so confusing..
3
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1answer
38 views

Question about definition of random sample

In my statistics class, we're just beginning to talk about (point) estimation. I have a small question that might actually be due more to notation/definition than anything very conceptual: Say you ...
0
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1answer
29 views

Is there a statistical differing interpretation between match and fit?

I've seen the terms matching/match and fitting/fit used almost interchangeably when discussing models goodness of fit, observed vs simulated data matching, etc. Is there a difference in ...
7
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3answers
1k views

What does “curvilinear” mean?

As far as I can tell, curvilinear is defined vaguely but means the same as nonlinear. Is that correct? Or does curvilinear have a distinct definition?
2
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1answer
244 views

What is the difference between sample and outcome? (plus events and observations)

I was sure that these are the same things but I do not get the difference reading about mass probability function Suppose that $X: S → A (A \subseteq R)$ is a discrete random variable defined on ...
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0answers
34 views

what dates to use to calculate length of follow up

I am dealing with a set of surgery patient data, have the date of surgery, date of discharge, and date of the last follow-up visit. I am wondering that for calculating the duration of follow-up, do I ...
4
votes
1answer
113 views

Has the parameter $\frac{1}{\sqrt{2(n-1)}}$ a name?

Has the parameter $\displaystyle \frac{1}{\sqrt{2(n-1)}}$ a name? $n=\text{number of observations}$
1
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1answer
35 views

Explanation of order of integration in the context of cointegration

Please explain the meaning of 'order of integration' when talking about cointegration. An explanation with some examples would be great.
1
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1answer
10k views

What is the difference between a parametric test and non-parametric tests? [duplicate]

Please explain the difference between a parametric and a non-parametric test. Do all data mining techniques come under the non-parametric category?
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0answers
40 views

Configural frequency analysis

What do you think about configural frequency analysis? http://en.m.wikipedia.org/wiki/Configural_frequency_analysis I personally love the idea to extract types and antitypes in heterogenous samples ...
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0answers
44 views

Window models in stream data processing

Reading about data stream clustering I met the next terms: landmark window model, sliding window model, damped window. As to sliding window it's clear - oldest data escape the scope, the new data ...
0
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1answer
60 views

What is the $p$ in Cook's distance?

In the equation for Cook's distance: $$D_i = \frac{\sum_{j=1}^{n}(\hat{y}_j - \hat{y}_{j(i)})^2}{p MSE}$$ the value of $p$ is defined as "the number of fitted parameters in the model." What does ...
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2answers
90 views

What are “second-order dependencies” and “higher order dependencies” in the data?

I am reading A Tutorial on Principal Component Analysis by Shlens, 2014, and it mentions these two notions: "second-order dependencies" and "higher order dependencies". I could not find any clear ...
0
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1answer
36 views

What is a seasonality of a data stream ? How to use it to estimate a stream attributes ?

I am trying to understand what is the rigorous definition of seasonality is, but couldn't find it. Is it a mathematical tool at all? I need to analyze a stream coming from one source and be able to ...
1
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1answer
257 views

Simple definition of elliptical distribution

I'm looking for a simple explanation of what an elliptical distribution is and how it differs from a non-elliptical distribution. My knowledge of stats is very basic; Wikipedia was not much help on ...
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0answers
27 views

Question about the frequency definition of probability

In the book, it is written that the relative frequency or the frequency ratio gradually tends to become more or less constant as N becomes larger and larger. It is also mentioned that this is an ...
2
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0answers
61 views

What is the null hypothesis in the definition of Sensitivity and Specificity?

I have hard time to understand that what is the null hypothesis in the definition of Sensitivity and Specificity here? I'm student of Statistics and from my little knowledge in this field I can see ...
10
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2answers
7k views

Is variation the same as variance?

This is my first question on Cross Validated here, so please help me out even if it seems trivial :-) First of all, the question might be an outcome of language differences or perhaps me having real ...
8
votes
1answer
142 views

What exactly is called “principal component” in PCA?

Suppose $u$ is the vector that maximizes the variance of the projection of the data with design matrix $X$. Now, I have seen materials that refer $u$ as the (first) principal component of the data, ...
0
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1answer
177 views

Why does doing LDA on a outer product of input matrix gives same result as doing PCA of the input matrix?

Why does doing Linear Discrimenant Analysis (LDA) on a outer product of input matrix gives same result as doing Principal Component Analysis (PCA) of the input matrix? Not exactly sure where this ...
5
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2answers
144 views

Definition of statistical model in case of hierarchical model

In wikipedia the definition of a parametric model is the following: A parametric model is a collection of distributions, each of which is indexed by a unique finite-dimensional parameter: ...
1
vote
1answer
236 views

Difference in meaning of these terms: Dataset vs Corpus

I have a question pertaining to definition of terms that I couldn't find answer for. What's the difference between Dataset and Corpus? I've seen them being used almost interchangeably. My ...
5
votes
1answer
164 views

Deviate vs. Variable

What is the difference between a multivariate normal random deviate and a random variable? More specifically, I suppose, what exactly is a deviate?