Smr Derivation And Properties

SMR Derivation and Properties

Use this for theory integrity. SMR is a methods journal: a property that is asserted but neither derived nor argued is the most common reviewer wound. You do not need Econometrica-level generality, but every claim about what the method does must be traceable from stated assumptions.

The traceable chain

A reader should be able to follow, in order:

1. Target / estimand — the population quantity or hypothesis the method addresses.
2. Assumptions — each one labeled by the role it plays (existence, identification, consistency, asymptotic normality, finite-sample approximation, computation).
3. Estimator / statistic — the exact object computed from data.
4. Properties — bias (finite-sample and asymptotic), consistency conditions, efficiency relative to the incumbent, the variance estimator, and the regime where it holds.
5. Failure boundary — where the assumptions fail and what happens to the property there.

If any link is missing, that link is what the report will quote back.

Assumption ledger

Build this before rewriting the theory section:

Assumption | Role | Where used | Empirical/sim check | If weakened

Use it to (a) delete decorative assumptions, (b) expose missing ones, and (c) tie each assumption to something a sociologist can recognize in real data. SMR readers are applied methodologists: a condition stated only for proof convenience must say whether it can be relaxed and whether the simulation probes its boundary.

Property claims at SMR (what reviewers expect)

• Consistency / unbiasedness: state the conditions, not just the conclusion. "Consistent under MAR and correct outcome model" is a claim; "performs well" is not.
• Efficiency: relative to what? Name the comparison estimator and the regime.
• Inference validity: give the variance estimator and the conditions under which its coverage is nominal; SMR papers routinely live or die on coverage, not point estimates.
• Robustness: be explicit about what the method is and is not robust to (e.g., doubly robust to one of two models, not to both failing).

Proof economy for a methods-journal audience

• Keep the main argument legible in the body; route long algebra to an appendix, but never hide a load-bearing step there with only "it can be shown."
• Match the rigor to the claim: a closed-form bias correction needs a derivation; an evaluation paper needs a clear analytical reason the failure occurs, not a theorem for its own sake.
• Separate theorem (proved), result (derived under stated conditions), and finding (observed in simulation). Label them so a reviewer never has to guess the evidentiary status.

Pair every property with a finite-sample check

Each analytical property should name the simulation exhibit that demonstrates it at realistic sample sizes — SMR treats an unpaired asymptotic claim as unfinished. Hand the boundary cases to smr-simulation-studies so the Monte Carlo stresses exactly the assumption most likely to fail.

Checklist

• Estimand, assumptions, estimator, and properties are stated in that order before derivations.
• Each assumption is labeled by role and tied to a recognizable data feature.
• Consistency/efficiency/inference claims state conditions and the comparison method.
• The variance estimator and its coverage conditions are given.
• The failure boundary is stated, not hidden.
• Each property names the simulation exhibit that checks it in finite samples.
• Proved / derived / simulated claims are labeled distinctly.

Anti-patterns

• Asserted properties: "our estimator is consistent and efficient" with no conditions or proof.
• Decorative assumptions: regularity conditions never used or never tied to data.
• Hidden load-bearing steps: a key derivation replaced by "it can be shown."
• Evidence laundering: simulation regularities phrased as theorems.
• Coverage silence: a new estimator with no variance estimator or coverage argument.

Output format

[Theory status] defensible / needs repair / not ready
[Estimand] <population quantity or hypothesis>
[Critical assumptions] <assumption -> role>
[Properties claimed] <bias / consistency / efficiency / coverage, with conditions>
[Property gaps] <missing condition, variance estimator, or failure boundary>
[Next SMR skill] smr-simulation-studies