Statistical Inference

Definition of a random sample, statistical model, and likelihood. Definition and properties of estimators and sufficient, ancillary, and complete statistics. Point estimation: comparing estimators in a decision-theoretic framework (loss functions, risk, mean squared error) and optimality results (Uniform Minimum Variance Estimators, Fisher's information, Cramér-Rao bound). Hypothesis testing: comparing testing procedures and constructing optimal tests within the Neyman-Pearson framework. Tests based on the likelihood ratio. Confidence intervals: construction based on inverting tests. Asymptotic considerations: consistent and asymptotically efficient estimators. Likelihood-based asymptotic tests and confidence intervals.