By 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