Università Roma Tre

Introduction to statistics: random sampling of finite and infinite populations. Definition of the statistical model and the concept of statistics. Example of statistics. Properties of statistics: sufficient, minimal and complete statistics.

Point estimators: method of moments, maximum likelihood estimators and Bayes estimators. EM algorithm.

How to evaluate estimators: bias, consistency and mean square error. UMVU estimators and efficient estimators.

Confidence interval: the concept of pivotals, asymptotic methods and the delta method.

Hypothesis testing: definitions, likelihood ratio test and duality with confidence interval. Uniformly most powerful tests.

Non-parametric methods: Goodness-of-fit test for discrete and continuum variables, contingency tables and Kolmogorov-Smirnov test.

Other topics: analysis of variance (ANOVA), linear regression, generalized linear regression and logistic regression.

Statistical Inference
Casella e Berger
Duxbury
2nd edition.