Parametric statistical models

Depends on

• Statistical experiments

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
• The observed first time and cause do not identify the latent joint failure-time law Counterexample
• Bayesian model as a prior and sampling kernel Definition
• Binding function and indirect-inference target Definition
• Covariance and correlation principal component analysis Definition
• Density targets and the kernel density estimator Definition
• Estimands on a statistical model Definition
• Estimator sequences in IID experiments Definition
• Filtering, predictive, and smoothing laws in a finite-horizon state-space model Definition
• Finite populations and sampling designs Definition
• Finite-group hierarchical Bayesian model Definition
• Fixed-design linear regression model Definition
• Identifiability of an estimand Definition
• Observational equivalence Definition
• Parametric survival and reliability models Definition
• Quadratic-mean differentiability at a parameter Definition
• Scientific statistical model contracts Definition
• The iid multivariate-normal sample and covariance conventions Definition
• Wald, score, and likelihood-ratio statistics for regular nulls Definition
• An unvalidated calibration offset leaves the true quantity unidentified Example
• Biological units, repeated visits, and technical assay replicates Example
• Identifiable Bernoulli model and parameter target 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
• Observed-data likelihood under a response model Lemma
• Sample-centered covariance is a measurable statistic and estimator Lemma
• The observed law need not identify the latent-error variance split Proposition
• A zero inclusion probability prevents total identification and universal unbiased estimation Theorem
• Asymptotic linearity and normality of a regular MLE Theorem
• Backdoor adjustment identifies an interventional law 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
• Gaussian variance-component identifiability is covariance-map injectivity Theorem

…and 6 more results.

Dependency tree · two levels

5 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, §§1.3.6 and 1.4.1, PDF pp. 20–23 (standard reference, not scraped)
• Charles J. Geyer, Stat 5421 Lecture Notes: Exponential Families, §6, PDF pp. 6–7 (standard reference, not scraped)