Università Roma Tre

Random variables and their distribution, moment generating function, mean variance and covariance.
Random sampling model and statistical model.
Statistics: concept, examples, sufficient statistics.
Point estimators: definition and desired properties, moments, maximum likelihood and Bayes.
Computational methods: Newton-Raphson, EM algorithm
Improving an estimator: Rao-Blackwell, UMVU estimator, full statistic, Lehman-Scheff ́e II and Cramer-Rao
Confidence intervals: intuitive, pivotal quantity, IC for Bayes and asymptotic IC.
Hypothesis testing: likelihood ratio, pivotal quantity test (Z and T test), duality with IC, UMP, Neyman-Pearson and Karlin-Rubin tests.
Non-parametric methods: goodness-of-fit, contingency table, Kolmogorov-Smirnov and ranking tests.
Analysis of variance (ANOVA) and F.
Regression: linear, multiple linear, generalized linear and Logistic / Poisson

Statistical Inference, Casella e Berger, 2nd Edition, Duxbury Advanced Series.

Additional reference:
Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi