Statistical estimator

Mathematical statement

On a finite parameter model with one common sample space, the statistic table depends only on the observation. Expectations can be computed under each parameter law, but no unbiasedness, consistency, sufficiency, identifiability or posterior claim follows here. Full sampling distributions are a later object.

Representative formula (exact TeX)

E(X)

Assumptions

• The finite sample space is shared and the parametric model has qualified.
• Every outcome has exactly one statistic value, with no unknown-parameter index in that statistic.

Symbol scope

• E — statistical estimator
• X — sample observation

Intuition, definition, and misconceptions

The estimator is a function; the estimate is its observed value.

That function must not depend on the unknown parameter.

Statistical properties and the sampling law need separate evidence.

Do not confuse an estimate with the estimator or insert the unknown parameter into its definition.

Adopted derivation guide

The original MKO is retained. The guide has its own append-only revision and verification boundaries, not a new Lean proof.

Prerequisites

• Parametric statistical model — Each parameter supplies a law.
• Real random variables on finite sample spaces — A statistic is a function of the sample.
• Sample space — The statistic has a total observation domain.

Verification boundary

Only a finite total statistic and parameter-specific expectations are checked; statistical properties are not inferred.

not_formalized

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

Next obligation

Add sampling distributions, bias and variance.

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.