Chiandotto Bruno (2017). Inferenza statistica. Dispense, DISIA
Mood M. Alexander, Graybill A. Franklin, Duane C. Boes. (2003). Introduzione alla statistica. McGraw - Hill.
Mood M. Alexander, Graybill A. Franklin, Duane C. Boes. (1974). Introduction to the Theory of Statistics. McGraw - Hill.
Pace Luigi, Salvan Alessandra. (2001). Introduzione alla statistica-II. Inferenza, verosimiglianza, modelli. Padova: CEDAM.
The aim of this course is to introduce students to the theory and practice of statistical inference
and to the related computational strategies and algorithms.
Moreover the course aims to develop
students' expertise to analyze inferential problems selecting the appropriate inferential methods, to implement the analyses in R, and to properly interpreter and describe the results of the analyses.
Basic knowledge of algebra, maths and statistics
Lectures, sessions of exercises and labs
Additional teaching materials will be provided during the course through the e-learning platform
Type of Assessment
Written and oral exam, which will also require the analysis of data with R
Introduction to statistical inference: Statistical models; Parametric statistical models;
Exponential families; Regular exponential families; Location and scale families; Experiment
and statistical model; Sampling from infinite population; Random sample and observed
sample; Statistical models for random samples; An introduction to the main inferential
problems; Inferential approaches: an overview.
Statistics and sampling distributions: Statistics; Sampling distributions;
Sum, mean and sampling variance for random samples; Sufficient statistics;
Ancillary statistics; Complete statistics; Basu's theorem.
Point estimation: Estimators (minimax estimators, method of moments estimators, maximum Likelihood estimators); Properties of estimators (unbiasedness, efficiency);
Fisher information; Cramér-Rao inequality; Rao-Blackwell's theorem; Asymptotic theory (consistency,
estimators with Normal asymptotic distributions, asymptotic efficiency); Properties of
Likelihood estimators; Properties of method of moments estimators.
Testing of Hypotheses: Formulation of the hypothesis testing problem; The Neyman–Pearson
Theorem; Likelihood ratio tests; Most powerful tests; Unbiased test; Asymptotic tests;
Interval estimation: Pivotal quantities and method of pivots; Method of test inversion;
Methods of evaluating interval estimators; Approximate maximum likelihood intervals.
Miscellanea: The Delta method; Bootstrap; The Newton-Raphson algorithm; The EM
algorithm; Introduction to mixture models; Introduction to nonparametric statistical inference; Introduction to Bayesian inference.