# Questions tagged [statistical-inference]

The area of statistics that focuses on taking information from samples of a population, in order to derive information on the entire population.

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### In Bias-variance decomposition of Mean Squared Error, why must one assume the error $\epsilon$ has $\text{Var}(\epsilon) = \sigma^{2}$?

I'm trying to understand bias-variance decomposition. Proofs of the decomposition often start by stating that the data conforms to the statistical model $y = f(x) + \epsilon$, where $\epsilon$ is an ...
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### How to do Hypothesis testing?

I have two time series data. Electric vehicle demand at a station (whole number time series) every hour called "Clstr 175" Weather description (categorical time series) at the station every ...
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### DIC, WAIC: non-invariant posterior mean, "negative effective dimension"

I am going through some lecture notes that unfortunatly do not contain any examples. "However, the DIC relies on the posterior mean as a point estimate, is not invariant with respect to ...
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### Coincise introduction to background for semiparametric statistics

I plan to study the theory behind Targeted Maximum Likelihood Estimation, Doubly Robust Estimation, and Semiparametric Theory. I have a background in bioinformatics: I took courses in basic linear ...
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### Definition about probability mass function by Rober V. Hogg

The following definition of pmf is on page51 from Probability and statistical inference by Robert V. Hogg, etc. The pmf $f(x)$ of a discrete random variable X is a function that satisfies the ...
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Can Strong LLN and Weak LLN apply to continuous distributions? Or it can only apply to discrete distributions? Representation of LLN: $X_1,X_2,\ldots,X_n$ are i.i.d, and their expectation values are ...