Questions tagged [notation]
For questions about statistical notation and mathematical notation used in statistics.
465
questions
0
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0answers
20 views
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
$L\left(\Omega_{e}\right),$...
3
votes
1answer
40 views
How to properly write negative binomial regression?
I am modeling the number of likes in a given hour, where $y_t$ gives the number of new likes on an item in the hour $t$, and seeing how the slope changes after a certain break-point. I assume that $...
0
votes
0answers
22 views
Is this the correct notation for the logistic regression I am trying to describe?
I'm looking for some confirmation that this is the right notation to describe my logistic regression (or advice on how to fix it).
I am performing association tests between a binary disease outcome a ...
3
votes
4answers
130 views
+50
confusion about individual notation
Let's say I am trying to estimate the regression of y on x:
$y= x \beta + \epsilon$
so when moving to regression frameworks, I often see people use the individual notation:
$y_i = x_i \beta + \...
1
vote
0answers
16 views
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 ...
8
votes
2answers
212 views
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: ...
0
votes
1answer
54 views
Variance of $\frac{\sum{X_i}}n$, where $X_i$'s are i.i.d. Bernoulli random variables
It's abou Example 10.1.14 from Casella (2nd ed) For a random sample $X_1, \dots, X_n$, each having Bernoulli distribution ($P(X_i=1)=p$), we know $\mathrm{Var}_X=p(1-p)$.
It's said $\mathrm{Var}_p\hat{...
0
votes
1answer
26 views
Mathematical notation for R::tail(X, n = 1)
Given a sorted vector $X$, the minimum is expressed symbolically as $X_{(1)}$ and the maximum as $X_{(n)}$.
Supposing for a given unsorted vector $Y$, we wanted to know the last value in said vector, ...
13
votes
2answers
1k views
Why are density functions sometimes written with conditional notation?
I keep seeing density functions that don't explicitly arise from conditioning written with the conditional sign:
For example for the density of the Gaussian $N(\mu,\sigma)$ why write:
$$ f(x| \mu, \...
0
votes
0answers
10 views
Does this conditional probability notation mean “except /”excluding adjacent pairs"?
For the following description of the Pairwise Markov property I would anticipate the formulation to indicate
All $X_u$ and $X_v$ are independent when considering ...
0
votes
0answers
11 views
trying to understand repeated sampling with individual error terms, regression errors, intuitively
in the model $Y_i = \beta X_i + \eta_i$,
for consistency unbiasedness, it is typically assumed $E[\eta_i|x_i]=0$.
since each error for every i in the data is its own random variable, this then must ...
0
votes
0answers
15 views
Likelihood function and sampling distribution symbol
I read a introductory stat book that the likelihood function has symbol like , e.g., L(theta, x); while the sampling distribution has the symbol like f(x,theta). May I ask does anyone know whether the ...
1
vote
0answers
38 views
Nested multilevel model notation
I am fitting the following logit model in lme4 (R):
dummy ~ individual_level_var1 + state_level_var2 + country_level_var3 + (1 | country/state)
The model is fitted ...
0
votes
1answer
27 views
Simple notation question: pdf for mle of uniform?
I have simple notation question related to pdf for mle of uniform $U(0,\theta)$.
Given following pdf $f(\hat{\theta}_{MLE}) = \frac{n \cdot \hat{\theta}_{MLE}^{(n-1)}}{\theta^n} $ , I'm confused ...
0
votes
1answer
26 views
SVM formula variations
I was reading about SVM in Wikipedia and saw that the formula was written like this (with minus):
$$
\vec{w} \cdot \vec{x} - b = 0
$$
While other sources have it like this (with plus):
$$
\boldsymbol {...
1
vote
1answer
19 views
Question on notation (t-statistics)
Which one is correct:
"Coefficients are shown in bold. T-statistics are shown in parentheses."
or
"Coefficients are shown in bold. t-statistics are shown in parentheses."
Or are ...
0
votes
0answers
18 views
Algebraic notation of my longitudinal mixed effects model
I have fit two models in R using the NLME package. The first one includes time varying variables and the second one time invariant variables.
Model 1:
Y ~ Time_measured, random = ~ Time_Measured|ID
...
0
votes
0answers
12 views
F-test for homogeneity with infinite degrees of freedom
I'm trying to replicate a previous analysis that is lacking in documentation. I am comparing estimated values between weeks to evaluate whether I should combine groups for analysis. The previous ...
1
vote
1answer
32 views
Notation for independence of potential outcomes
If we say (binary) treatment status, t is independent of potential outcomes, $\{y_1,y_o\}$, it is usually writing as
$t_i \perp \!\!\! \perp \{y_{i1},y_{io}\}$ .
I take this to mean intuitively, for ...
0
votes
1answer
27 views
What does x(#) mean in government statistical publications?
I am analyzing some UNESCO data on education and I came across the notation of "x(10)" or more generally "x(somenumber)" as cell values in their official spreadsheets such as this ...
4
votes
0answers
73 views
What does it mean to take the expectation with respect to a probability distribution?
I see this expectation in a lot of machine learning literature:
$$\mathbb{E}_{p(\mathbf{x};\mathbf{\theta})}[f(\mathbf{x};\mathbf{\phi})] = \int p(\mathbf{x};\mathbf{\theta}) f(\mathbf{x};\mathbf{\phi}...
0
votes
1answer
38 views
Question about estimating the standard error of the regression- notation and intuition
in a standard linear regression frame work:
$y_{i}=\beta x_i + \epsilon_i$
when calculating standard errors, we find an unbiased and consistent estimator of $var(\hat{\beta})$. Assume spherical errors....
3
votes
2answers
43 views
Help regarding the notation used in certain expression for the pdf
The probability density function of a certain random variable is given by $$ \begin{aligned}g(t)&=4 n(n-1)\\&\int_0^1 x(x+t)1(x+t<1)[(x+t)^2\,1(x+t<1)+1(x+t\ge1)-x^2]^{n-2}\, dx\,1(t>...
0
votes
0answers
17 views
Confusion on vector, matrix notation on research papers and the need of row normalization
I attempt to understand the formulation of dictionary learning for this paper:
Depression Detection via Harvesting Social Media: A Multimodal Dictionary Learning Solution
Multimodal Task-Driven ...
0
votes
1answer
60 views
Question about intuition of exogeneity with individual notation
In econometrics, we typicall assume exogeneity as, starting with $y = x\beta + \epsilon$:
$E[\epsilon|x]=0$.
I always intuitively thought about this in an abstract sense, away from the individual ...
1
vote
0answers
15 views
Notation in “Fast Computation of Multivariate Kernel Estimators” by M. P. Wand
I'm new to kernel estimation methods and I've reading the paper "Fast Computation of Multivariate Kernel Estimators" by M. P. Wand.
Particulary on page 434, it says "Let $(X_1, Y_1), ......
0
votes
0answers
17 views
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 ...
1
vote
1answer
14 views
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 ...
1
vote
1answer
60 views
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 $q \times 1$, ...
5
votes
1answer
68 views
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, ...
1
vote
2answers
46 views
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.
...
6
votes
1answer
642 views
Meaning of vertical bar | in loss function?
Does anyone know what the vertical bars in these equations here mean?
Specifically, these?
3
votes
1answer
69 views
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 ...
0
votes
0answers
20 views
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 "$Z_t = (U_t , X_t , Y_t )$ ...
-1
votes
1answer
119 views
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 $z(p/2)$?
2
votes
1answer
52 views
Confused about notation on “All of Statistics” bootstrap
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(...
-1
votes
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 ...
2
votes
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 ...
0
votes
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 $f$
$$
f = \left\{\begin{matrix}
\mathcal{X}\mapsto\mathcal{Y}\\
X \mapsto \...
2
votes
1answer
87 views
$\epsilon$ vs residual
In section 3.2.3 of Elements of statistical learning, the authors wrote in equation 3.23
$$
Y = X\beta + \epsilon
$$
but didn't give a name for $\epsilon$. Then it states that the "residuals" are
$$
...
0
votes
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 $...
0
votes
1answer
28 views
Why are there two ways to write PDF and CDF functions?
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 ...
-1
votes
1answer
29 views
sign symbol above or below the sigma operator
the below two expressions are the same according some references, so, my question is, why does it change the sign in $Y_{i+k}$ or $Y_{i-k},$ when there is a plus or a minus sign above or below the $\...
4
votes
1answer
52 views
What do the letter and the subscript in the Shewhart's control chart constants ($A_2, A_3, c_4, c_5, \ldots$) mean?
The expected value of the sample standard deviation is
$$E(s) = c_4(n)\sigma$$
where
$$
c_4(n) = \sqrt{2\over n-1}{\Gamma({n\over2})\over\Gamma({n-1\over2})}
$$
The page on Wikipedia led me ...
9
votes
1answer
545 views
Why is the Beta Distribution Called the Beta Distribution?
In my research, I've been unable to find a historical explanation for why the Beta distribution has the name it does. I'm aware of what Wikipedia says about how it got its name, but so far I haven't ...
2
votes
1answer
33 views
Causality: Models, Reasoning, and Inference: Notation Question Concerning Graphoids
$\newcommand{\ci}{\!\perp\!\!\!\perp\!}$On page 11 of the book in the title, Pearl introduces the Dawid notation for conditional independence: $(X\ci Y|Z)_P$ if and only if $P(x|y,z)=P(x|z)$ for all ...
1
vote
1answer
67 views
What is “LASSO aggression”?
I found a paper that stated in the methods section that they ran "LASSO aggression". At first, I thought it was a funny typo but then I did a Google Search:
Google search
and found 187 sources ...
-1
votes
1answer
29 views
Is this statistically significant?
F value 42.341
P value 1.6E-07
F c.v 3.554
The p-value is more than 0.05 but the F value is significant. Or is the p-value considered small since it has E?
0
votes
1answer
30 views
Help with notation!
I have calculated the average absolute difference with the accompanying absolute standard deviation. I write this as e.g.:
|0.05 +- 0.12|
Is this correct?
I ...
2
votes
1answer
115 views
Is there a standard symbol for standard error?
The mean of a dataset is often represented by the Greek letter $\mu$, and the standard deviation of a dataset is often represented by the Greek letter $\sigma$. But what about the standard error? I've ...
