# 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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0answers
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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://...
0answers
21 views

### 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 ...
0answers
17 views

### 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 ...
0answers
37 views

### Null hypothesis definition

why do we use H0: μ ≥ μ0 in a left tailed test and try to reject H0 rather than using H0: μ ≤ μ0 and trying to prove H0 is true? thanks
0answers
20 views

### Definition of the word “embedding”

The mathematical definition of the word "embedding" requires the mapping to be injective, so in that context one speaks of, for example, embedding real numbers in complex numbers (ie, ...
0answers
18 views

### Can the distribution of a pivot depend on known parameters?

I have a question about the distribution of a pivot. Different sources give slightly different definitions of a pivot. Some of them define it as a random variable $Q(\mathbf{X}, \theta)$ whose ...
0answers
79 views

### Decision Theory: Why is it called a “least favorable prior”?

I'm currently reading the chapter on Statistical Decision Theory in Larry Wasserman's "All of Statistics". Reading the section 13.4 about Minimax Rules he introduces the so called Least ...
0answers
15 views

### What is a Figure of Merit in statistics?

Papers published on the arXiv often mention the notion of Figure of Merit (FOM). Can you explain what a Figure of Merit is, how it is used and what are its relations to statistics?
0answers
30 views

### For a generative model, how is modelling p(X,Y) equivalent to modelling P(X|Y=y)?

On the Wikipedia page for generative models it gives the following definitions of a generative model: (X is an observable variable, Y is the target variable) 1) A generative model is a model of the ...
0answers
12 views

### Clarification regarding comonotonic random variables

According to wikipedia, an equivalent definition of a comonotonic random vector is: A $\mathbb{R}^n$-valued vector is comonotonic iff it agrees in distribution with a random vector where all ...
3answers
96 views

### What are Global minima and Local minima in Machine Learning?

What are Global minima and Local minima in Machine Learning? How is it used?
0answers
22 views

### Can I define a random sample as a collection of random variables?

I have been reading a few posts like this one (What is the difference between random variable and random sample?) on the subject so I'd like to make sure my understanding is correct. Let us say I ...
1answer
60 views

### What is meant by divergence in statistics?

I have learned about the Intuition on the Kullback-Leibler (KL) Divergence as how much a model distribution function differs from the theoretical/true distribution of the data. The two most important ...
2answers
76 views

### Likelihood $L(\theta; \mathbf{y})$: Is $\theta$ a vector of parameters or is it a single parameter?

I have the following definition of likelihood: Let $y_1, \dots, y_n$ be a sample of observations taken on corresponding random variables $Y_1, \dots, Y_n$ whose distribution depends on the parameter(...
1answer
56 views

### Definition of statistical significance

Consider the following definition of statistical significance: Statistical significance is a characteristic of a statistic viewed in light of an (implicit or explicit) null hypothesis and a given ...
2answers
590 views

### Is a spline interpolation considered to be a nonparametric model?

I am aware of the basic differences between nonparametric and parametric statistics. In parametric models, we assume the data follows a distribution and fit it onto it using a fixed number of ...
0answers
22 views

### Should I say “copula” or “copula function”? Is the latter superfluous?

I am writing a paper involving copulas and have been thinking of whether I should say "copula function" or just "copula", as I am not sure whether the term "copula" ...
1answer
125 views

### Splines: relationship of knots, degree and degrees of freedom

Could one explain how these three parameters change the behaviour of this "wiggle curve" In particular, I am trying to understand b-splines and m-splines. My limited understanding is as ...
1answer
35 views

### Seeking clarity regarding kernels

With regards to Bayesian statistics, I understand the kernel of a probability density function (pdf) or probability mass function (pmf) to be the form of the pdf or pmf in which any factors that are ...
1answer
46 views

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### What does this mean? ($\boldsymbol{I}_{\theta, \infty}(x_i)$) [duplicate]

In my studies I came across this There is some more to this answer but for the purpose of this question lets leave it at that. I can't figure out what $\boldsymbol{I}_{\theta, \infty}(x_i/i)$ is and ...
0answers
81 views

### What is it called when a random variable is weakly greater than another for all elements of the sample space?

Suppose I have random variables $(X_1,X_2)$ defined on a probability space $(\Omega, \mathcal{F},P)$ such that for any element $\omega \in \Omega$, $X_1(\omega) \geq X_2(\omega)$. I'm looking to work ...
0answers
18 views

### How is an 'ogival function' defined?

Reading on a paper on factor analysis and measurement invariance I find the description of some functions as 'ogival' functions. In Google I find it referenced mostly in papers from the '70s and '80s....
1answer
882 views

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### Defining statistical significance under methods: using alpha or p?

Two options: Statistical significance was defined as alpha = 0.05, and all tests were 2-sided. Statistical significance was defined as p < 0.05, and all tests were 2-sided. Are both of them ...
0answers
107 views

### What is gradient correlation?

I came to cross a type of correlation that I haven't heard before --- what is gradient correlation? Does the gradient correlation function range from 0 to 1 just like the regular Pearson's correlation?...
1answer
632 views

### What is Asymptotic Independence

What does it mean if two random variables are asymptotically independent? And how would you prove that they are?