Mathematics / advanced
Asymptotic statistical theory
Derive large-sample approximations while checking regularity, local alternatives, efficiency, and bootstrap validity.
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Module 01 advanced
Asymptotic statistical theory
Derive large-sample approximations while checking regularity, local alternatives, efficiency, and bootstrap validity.
- 01
Consistency and uniform laws of large numbers
Control an entire random criterion before trusting its optimizer.
32 min - 02
The delta method and functional delta method
Propagate weak limits through smooth maps while respecting the tangent space.
32 min - 03
Asymptotic normality of M-estimators
Separate objective consistency, local curvature, score noise, and sandwich variance.
32 min - 04
Z-estimators and estimating equations
Linearize a population root without demanding a smooth sample equation.
32 min - 05
Local asymptotic normality
Approximate a regular experiment through local likelihood ratios.
32 min - 06
Contiguity and Le Cam’s lemmas
Transfer local limits by checking likelihood mass and joint convergence.
32 min - 07
Asymptotic efficiency and convolution bounds
State what regularity rules out before comparing an estimator with information.
32 min - 08
Likelihood-ratio asymptotics and boundaries
Check the null geometry before assigning chi-square degrees of freedom.
32 min - 09
Bootstrap consistency and counterexamples
Compare conditional laws and expose a persistent resampling atom.
32 min - 10
Semiparametric influence functions and efficient scores
Use tangent-space projection to separate target information from nuisance variation.
35 min