Statistical Inference Notes
A consolidated set of notes on statistical inference, including point estimation, maximum likelihood estimation, hypothesis testing, confidence intervals, and asymptotic inference.
Academic Notes · Statistics · Inference
Statistical Inference
Notes on point estimation, sufficiency, completeness, likelihood theory, hypothesis testing, confidence intervals, asymptotic inference, and related statistical tools.
Statistical Inference
Notes and drafts.
This section collects notes on classical and asymptotic statistical inference. The focus is on estimators, likelihood-based methods, tests, confidence sets, large-sample approximations, and the tools used repeatedly in theoretical and applied statistics.
Point Estimation
Notes on estimators, bias, variance, mean squared error, consistency, unbiasedness, efficiency, and comparison of competing estimators.
Sufficiency and Completeness
Notes on the factorization theorem, minimal sufficiency, completeness, ancillary statistics, Rao--Blackwellization, and Lehmann--Scheffé-type arguments.
Likelihood Theory
Notes on likelihood functions, score functions, Fisher information, maximum likelihood estimation, likelihood ratio tests, and asymptotic normality of MLEs.
Hypothesis Testing
Notes on null and alternative hypotheses, test functions, size, level, power, p-values, Neyman--Pearson testing, and uniformly most powerful tests.
Confidence Intervals and Confidence Sets
Notes on confidence intervals, coverage probability, pivotal quantities, asymptotic intervals, and the relationship between confidence sets and hypothesis tests.
Asymptotic Inference
Notes on convergence in distribution, Slutsky's theorem, the delta method, asymptotic normality, Wald tests, score tests, and likelihood ratio approximations.