statistical-theory-analysis

name	statistical-theory-analysis
description	Analyze theoretical properties of statistical methods under the formal formulation: identifiability, bias, variance, consistency, asymptotics, coverage, error bounds, robustness, and limitations.
metadata	{"category":"domain","trigger-keywords":"theory,proof,consistency,asymptotic normality,bias,variance,coverage,error bound,identifiability,robustness","applicable-stages":"4,5,6,7,8,9,10","priority":"1"}

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

## 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