AI agent skill · by @aiming-lab

Statistical Theory Analysis

Analyze theoretical properties of statistical methods under the formal formulation: identifiability, bias, variance, consistency, asymptotics, coverage, error bounds, robustness, and limitations.

Archived 2026-10-23 · Source updated 2026-08-19 · License: MIT. Check the original repository for the latest version.

SKILL.md instructions

# Statistical Theory Analysis

## Overview

Use this skill after method proposal and before final experimental comparison.
Theory is required as a stage even if the final output is a simulation paper.

## Theory Outputs

Depending on the topic, provide:

- Identifiability argument
- Bias or variance calculation
- Consistency statement
- Asymptotic distribution
- Coverage or calibration argument
- Risk or error bound
- Robustness analysis
- Sensitivity or impossibility result
- Counterexample showing failure outside assumptions

## Theorem Template

```markdown
## Proposition
Under assumptions A1-Ak, method M satisfies ...

## Proof Sketch
1. ...
2. ...
3. ...

## Interpretation
This predicts that ...

## Limitations
The result does not cover ...
```

## Experimental Predictions

Every theoretical claim should produce an empirical prediction when possible:

- Direction of metric change
- Condition under which the method should improve
- Stress condition under which it should fail
- Baseline it should outperform