# Statistical Theory Analysis

> Statistical Theory Analysis is an Agent Skill for research published in the aiming-lab/AutoResearchClaw repository on GitHub: a SKILL.md instruction file an AI agent can load to do this task.

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

- Skill name: `statistical-theory-analysis`
- Category: [Research](https://www.openparable.com/skill/research/1)
- Source: https://github.com/aiming-lab/AutoResearchClaw/blob/HEAD/external/agents/stat_research_agent/skills/statistical-theory-analysis/SKILL.md
- Repository: aiming-lab/AutoResearchClaw (13,814 GitHub stars when collected)

## SKILL.md

# 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

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Source: https://www.openparable.com/skill/research/statistical-theory-analysis (OpenParable). Cite the canonical URL above.