# Statistical Theory Analysis

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

- Skill: `gabrielmoreira/statistical-theory-analysis` (Agent Skill)
- Install (CLI): `npx skillmds@latest add gabrielmoreira/statistical-theory-analysis`
- Raw SKILL.md: https://api.skillmd.com/api/skills/gabrielmoreira/statistical-theory-analysis/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: gabrielmoreira (https://skillmd.com/u/gabrielmoreira)
- Updated: 2026-09-09
- Page: https://skillmd.com/skills/gabrielmoreira/statistical-theory-analysis

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# 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