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statistical-theory-analysis

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

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14,635
分类
数据
许可证
MIT
最近提交
2026年8月19日

external/agents/stat_research_agent/skills/statistical-theory-analysis/SKILL.md

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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

## 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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