# Estimator variance

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

At each theta, estimator variance is the second central moment of its sampling law around its own mean; it is not bias or MSE by itself.

mko-estimator-variance · definition · v0.10.0



## Mathematical statement

Keep sampling law, positive-mass support and mean at the same theta. Check Var_theta(T)=E_theta[(T−E_theta[T])^2]=E_theta[T^2]−(E_theta[T])^2 exactly. Zero variance means almost-sure constancy under that law, not equality with theta or unbiasedness.





## Representative formula (exact TeX)

V_theta(T)=E_theta(T^2)-E_theta(T)^2





## Assumptions


- The common finite sample space, complete exact parameter laws and fixed total statistic are supplied.
- All second moments are finite and use exact rational arithmetic.





## Symbol scope


- V_theta — estimator variance
- T — estimator





## Intuition, definition, and misconceptions

Variance is a parameter-indexed family.

The second-moment identity provides an exact cross-check.

Variance alone does not establish unbiasedness, consistency or MSE.

Zero variance does not imply unbiasedness, and variance is not MSE without checking the target and bias.





## Adopted derivation guide

[Same-law second and centered moment cross-checks](https://ocme.evemisslab.com/en/derivations/derivation-mko-estimator-variance-01/)The original MKO is retained. The guide has its own append-only revision and verification boundaries, not a new Lean proof.





## Prerequisites


- [Sampling distribution](https://ocme.evemisslab.com/en/mko/mko-sampling-distribution/) — Each parameter has a law of the estimator.
- [Variance in finite probability models](https://ocme.evemisslab.com/en/mko/mko-variance/) — The criterion is a second central moment.





## Verification boundary

Only complete finite sampling laws are handled; consistency across sample sizes requires a sequence model.

not_formalized

This does not mean the content is false; it means no replayable computational or formal evidence is registered yet.





## Next obligation

Add MSE and efficiency comparisons.





## Same-source structured data

This page and the interactive view use the same object and existing language edition; this adds no proof or human review.

[Canonical MKO JSON](https://ocme.evemisslab.com/data/mko/estimator-variance.json) · [Plain Markdown](https://ocme.evemisslab.com/en/mko/mko-estimator-variance/index.md)