# Statistical inference

ECTS: 9

Year: 1

Semester: I

Instructor: Fabrizio Cipollini, Carla Rampichini

Special r.v.’s: Bernoulli, Binomial, Poisson, Continuous Uniform, Normal, Gamma, Chi-squared, Student-T, Fisher-F, Beta. Transformation of r.v.’s. Introduction to Statistical Inference: Concepts of population, sample, parameter, statistics and estimator, statistics value and estimate, sample distribution of a statistic and related synthetic indices. Point Estimation: The Maximum Likelihood (ML) method. Properties of estimators. The Cramer-Rao bound. Asymptotic properties. Asymptotic properties of ML estimators. Interval Estimation: Definition of interval estimate (confidence interval), confidence level, size of the interval. The Pivot method for finding confidence intervals. Hypothesis testing: Motivations, framework, definitions of statistical hypothesis and of statistical test. Table of decisions, type I and type II errors, significance level and power of a test. The Neyman-Person lemma and ensuing remarks. Power of the test. The p-value. The likelihood ratio test. Linear Regression Model: Model definition and corresponding properties; the Least Squares (LS) and the ML methods for estimating the parameters. Deviance decomposition and R2 index; predictions of the conditional mean and of the dependent variable for a given value of the independent variable. Complementary Topics.