asymptotic-theory
M-estimation, influence functions, and semiparametric efficiency theory for causal inference
Profile →npx skills add brycewang-stanford/Auto-Empirical-Research-Skills --skill asymptotic-theory --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
What it does
This skill provides a rigorous framework for statistical inference and efficiency in causal inference, focusing on asymptotic properties of estimators, influence functions, and semiparametric efficiency theory. It outlines how to compute efficiency bounds, derive influence functions, and apply M-estimation theory to obtain consistent and asymptotically normal estimators, including double robust methods like AIPW and TMLE concepts.
How it works
The skill lays out concrete mathematical definitions and results for: semiparametric efficiency bounds, influence functions, and asymptotic distributions. It specifies how estimators achieve efficiency via EIF, and how double robustness yields consistency when either outcome or treatment models are correct. It includes procedural steps and R code sketches for computing the efficiency bound, estimating nuisance models (propensity and outcome), constructing the efficient influence function, and obtaining standard errors through sandwich estimators. It also provides guidance on variance estimation (analytic and bootstrap) and on performing inference (confidence intervals and hypothesis tests) using these asymptotic results.
When to use it
Use when evaluating or deriving asymptotic properties of estimators in causal inference settings, particularly for: M-estimation, influence functions, semiparametric efficiency, double robustness, variance estimation, and constructing CIs or tests based on asymptotic theory.
What it can touch
The skill references tools and code blocks for:
- R functions and models: glm, lm, and related regression tooling used to estimate nuisance components
- Calculation of efficient influence functions (EIF) and related quantities
- Sandwich variance components: Hessian and outer product of gradients
- Bootstrapping strategies: nonparametric bootstrap and influence-function-based bootstrap Note: It does not specify external software beyond these R snippets, and expects the agent to implement or adapt these computations in code.
Caveats
The material presents theoretical formulas and example code; outcomes depend on correct model specification and regularity conditions. The content includes complex concepts like EIF and semiparametric efficiency that require proper implementation and diagnostics in practice.
# Asymptotic Theory **Rigorous framework for statistical inference and efficiency in modern methodology** Use this skill when working on: asymptotic properties of estimators, influence functions, semiparametric efficiency, double robustness, variance estimation, confidence intervals, hypothesis testing, M-estimation, or deriving limiting distributions. --- ## Efficiency Bounds ### Semiparametric E
What does the asymptotic-theory skill do?
M-estimation, influence functions, and semiparametric efficiency theory for causal inference
How do I install it?
Run `npx skills add brycewang-stanford/Auto-Empirical-Research-Skills --skill asymptotic-theory --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From brycewang-stanford/Auto-Empirical-Research-Skills, a repository with 3,244 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.