# Questions tagged [notation]

For questions about statistical notation and mathematical notation used in statistics.

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### What does the “e” stand for in the notation of generalized likelihood ratio testing?

From Larsen and Marx, I read the following: For notational simplicity, we denote $\max _{\omega} L(\theta)$ and $\max _{\Omega} L(\theta)$ by $L\left(\omega_{e}\right)$ and $L\left(\Omega_{e}\right),$...
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### Notation question

In what follows $\Phi$ is the autoregressive polynomial obtained in estimating a (noncausal) VAR model, $Y_t - \Phi Y_{t-1}$ is the error term from the VAR process and $Y_{t-h} - \Phi Y_{t-h-1}$ is a ...
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### Is there a standard for statistical symbols?

Mathematics have ISO 80000-2:2019 which specifies mathematical symbols, explains their meanings, and gives verbal equivalents and applications. Is there an equivalent for statistical symbols? Edit: ...
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### Help deciphering strange notation in multiple hypothesis testing papers

I am not sure if this is the right venue for this question - if it is not, please let me know where I can post a question like this. In several multiple hypothesis testing papers, I have come across ...
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### What's the meaning of these notations in the cost fuction?

Except for the summation, I'm having a hard time figuring out the meaning of these notations. As I assume this is generic and the context is not that necessary, I'm here asking for help. (also, is ...
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### Doubts on how to write in vector

I know I can write a vector like this: $\beta = ( \beta_{1}, \dots, \beta_{p})^{\top}$ and $\rho = (\rho_{1}, \dots, \rho_{q})^{\top}$ by this way it have dimension $p \times 1$ and $q \times 1$, ...
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### If $\hat{a}=O_{p}(\sqrt{\frac{logn}{nh^b}}+h^c)$, what is $\hat{a}^2$ in terms of $O_{p}()$?

If $\hat{a}=O_{p}(\sqrt{\frac{logn}{nh^b}}+h^c)$, where $n$ is sample size, and $h$ is bandwidth that also depends on $n$. What is the order of $\hat{a}^2$ in terms of $O_{p}()$? More specifically, ...
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### Confused about the meaning of zero conditional mean with regressions analysis /exogeneity)

Usually the exogeneity assumption is states, given the vector E[$\epsilon$|x]=0. what this implies then is E[$\epsilon_i$|x$_i$]=0 for all i. The individual notation part is what is confusing me. ...
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### Meaning of vertical bar | in loss function?

Does anyone know what the vertical bars in these equations here mean? Specifically, these?
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### What's the definition of $O_{p}(\cdot)$ in the vector case?

For a scalar random sequence $X_n$, we write $X_n=O_p(a_n)$ if for every $\epsilon$ there exists $M_{\epsilon}$ such that $\limsup_{n}\Pr(|X_n/a_n|>M_{\epsilon})<\epsilon$. What's the extension ...
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### Dynamic Bayesian network notation

I am reading Murphy's thesis on Dynamic Bayesian networks [pdf download]. On page 14 (27 of the pdf) the variables within a DBNs are defined by a collection of nodes "$Z_t = (U_t , X_t , Y_t )$ ...
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### Normal quantile relation

If $X$ is a random variable having a standard normal distribution and $z(p)$ is the point having probability $p$ to the right of it. Is there any relation between $z(p)$ and $z(p/2)$?
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So I am currently reading "All of Statistics", and I am on the bootstrap chapter 8. I will transcribe a bit of the text to show what my confusion is. Basically, when he says that $T_n = g(... 1answer 63 views ### Notation about conditional expectation$E[Y|X]$Given$X,Y$real random variables, we know that$E[Y|X]$is X measurable and that there is a Lebesgue measurable function$f : \mathbf{R} \rightarrow \mathbf{R}$such that$E[Y|X]=f(X)$almost ... 1answer 158 views ### Using the letter P to represent an event It is known that in statistics$P(X)$represents the probability of$X$. My question: is it WRONG to use the letter$P$to represent an event, where$P(P)$represents the probability of$P$. For ... 0answers 21 views ### Notation of independence of random variables Consider$X = (X_1, X_2, X_3)$(random variables) with$X_1\sim \mu_1$,$X_2\sim \mu_2$,$X_1\sim \mu_3$and some function$f$$$f = \left\{\begin{matrix} \mathcal{X}\mapsto\mathcal{Y}\\ X \mapsto \... 1answer 87 views ### \epsilon vs residual In section 3.2.3 of Elements of statistical learning, the authors wrote in equation 3.23$$ Y = X\beta + \epsilon $$but didn't give a name for \epsilon. Then it states that the "residuals" are$$ ... 1answer 26 views ### Question about notation for constant variance In the context of linear regression where there is an assumption of "constant variance" I have read this: $$\mathbb{V}(\epsilon_i \mid X_i)=\sigma^2$$ But there are two ways I can read this. Either$...
I often see PDF and CDF functions written as either $f_X(x)$ or $f(x)$ for PDF or $F_X(x)$ or $F(x)$ for CDF. In what situations would you use either notation? Like what is the point of having ...