# Questions tagged [notation]

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

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### Notation to report the measurement of a parameter

The estimation of a parameter ($p$) is customary reported in Physics and other fields with, $p = \hat{p} \pm \Delta p$, where $\hat{p}$ is an estimator, and $[\hat{p} - \Delta p, \hat{p} + \Delta p]$ ...
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### Maximum likelihood for time series notation

I am going over the following slides where the likelihood for time series is formulated as (page 5): $f(y) = \prod_{i=2}^{n} f_{y_i|y_{i-}}(y_i|y_{i-}) f_{y_1}(y_1)$ I am not quite sure what the ...
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### Expectation conditional on a sigma algebra, what expectation does it refer to?

In a question like Intuition for Conditional Expectation of $\sigma$-algebra a concept like $E[X|\sigma(Y)]$ is used and I am puzzled about what sort of variable this actually is. Say we have a ...
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### Errors and residuals in simple exponential smoothing (state space form) in FPP textbook

I am reading Hyndman & Athanasopoulos "Forecasting: Principles and Practice" 2nd edition (FPP2). (I am aware that 3rd edition exists.) In the chapter about exponential smoothing, section ...
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### What is the most common notation to describe cyclostationary stochastic processes?

Can a cyclostationary stochastic process be described as: $\{X_t[i]:i\in\mathbb{N}\}\quad\forall~t\in\{1,2, \dots,T\}$ where variability at the $t^\text{th}$ index across all repetitions/seasons ...
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### Conditional Expectation Notation in ARCH Model

I'm new to ARCH models, and I have a question about the correct notation for expressing the conditional expectation of the return at time $t(r_t)$ given the information available up to time t-1. I'd ...
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### What does this notation mean? $\mathbb{P}_{x\sim \mathcal{D}}$: Clarification in the definition of generalization error $R(h)$

I was reading the book foundations of machine learning by Mehryar Mohri, Afshin Rostamizadeh and Ameet Talwalkar, and I came up with this definition of generalization error: I dont understand what ...
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### Notational confusion about conditional independence in Pearl 2009

First I read this definition which introduces $X$, $Y$ and $Z$ as sets of random variables. Definition (Pearl 2009) Let $V = \{V_1, V_2, \ldots \}$ be a finite set of variables. Let $P(\cdot)$ be a ...
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