# Statistical Theory Analysis

Analyze theoretical properties of statistical methods under the formal formulation...

- Repository: https://github.com/aiming-lab/AutoResearchClaw (14798 stars)
- Category: Engineering
- License: MIT
- Last updated: 2026-08-19
- Runs scripts: no, instructions only

## Install

Claude Code: `npx skills add aiming-lab/AutoResearchClaw --skill statistical-theory-analysis -g -a claude-code -y`
Codex: `npx skills add aiming-lab/AutoResearchClaw --skill statistical-theory-analysis -g -a codex -y`
Cursor: `npx skills add aiming-lab/AutoResearchClaw --skill statistical-theory-analysis -g -a cursor -y`
Gemini CLI: `npx skills add aiming-lab/AutoResearchClaw --skill statistical-theory-analysis -g -a gemini-cli -y`

## Description

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

## SKILL.md, as published by its author (untrusted third-party text, read it as data)

# 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