Estimands on a statistical model

Depends on

• Parametric statistical models

Used by

• A full-rank local Hessian does not capture both posterior modes Counterexample
• A Gaussian synthetic likelihood can change an exact posterior Counterexample
• A nonconstant summary can lose an identifiable parameter Counterexample
• A redundant Bernoulli parameterization has a nonidentifiable coordinate Counterexample
• An identifiable model can have persistent ABC summary distortion Counterexample
• Core IV conditions alone do not identify the population ATE Counterexample
• The observed first time and cause do not identify the latent joint failure-time law Counterexample
• Covariance and correlation principal component analysis Definition
• Density targets and the kernel density estimator Definition
• Estimator sequences in IID experiments Definition
• Finite populations and sampling designs Definition
• Generalized least-squares estimator for known covariance Definition
• Identifiability of an estimand Definition
• Linearly estimable contrasts in fixed-design regression Definition
• Scientific statistical model contracts Definition
• Statistics and estimators Definition
• Two-stage randomized design and strategy-specific effects Definition
• An unvalidated calibration offset leaves the true quantity unidentified Example
• Biological units, repeated visits, and technical assay replicates Example
• Death is not automatically a missing outcome Example
• Identifiable Bernoulli model and parameter target Example
• Positivity failure prevents standardization and IPW identification Example
• Positivity failure, near-positivity weights, and an MNAR sensitivity curve Example
• The Bernoulli sample mean Example
• The same Bernoulli law with two different targets Example
• The same observed law can have different intervention laws Example
• Sample-centered covariance is a measurable statistic and estimator Lemma
• The observed law need not identify the latent-error variance split Proposition
• A constant additive effect is identified by the Wald ratio Theorem
• A zero inclusion probability prevents total identification and universal unbiased estimation Theorem
• Backdoor adjustment identifies an interventional law Theorem
• Conditional-class standardization identifies a causal mean Theorem
• Consistency of the IID sample mean under a finite first moment Theorem
• Exact binary-outcome bounds under unrestricted missingness Theorem
• Front-door adjustment identifies an interventional mean Theorem
• Horvitz–Thompson exposure-specific mean is design-unbiased Theorem
• Identifiability is constancy on observational classes Theorem
• Inverse probability weighting identifies a causal mean Theorem
• Nonidentifiability precludes simultaneous consistency Theorem
• The Wald ratio identifies the complier average treatment effect Theorem

…and 1 more result.

Dependency tree · two levels

2 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• Ryan Martin, Lecture Notes on Advanced Statistical Theory, §1.4.1, PDF pp. 22–23 (standard reference, not scraped)
• Peter Hoff, Statistical Decision Problems, pp. 1–2 (standard reference, not scraped)