MATHEMATICAL STATISTICS

Description

The course will introduce students to the mathematical foundations of statistics. After providing a broad overview of basic tools that are commonly used in exploratory data analysis, lectures will be centered on the following main topics: point estimation, hypothesis testing, confidence regions and regression. Both frequentist and Bayesian approaches will be presented in detail. The methodological part of the course will be complemented by the discussion of real data applications. Descriptive statistics on univariate and bivariate samples. Sample means, variances and correlations Point estimation: Maximum likelihood estimators; Method of moments; Bayesian estimators Hypothesis testing: p-values and statistical significance, likelihood ratio tests, Wald Test, permutation test, Person’s chi-square test, multiple testing Confidence regions: definition and frequentist interpretation, pivotal quantities and construction of confidence intervals, Bayesian credibility regions Optimality theory: sufficient statistics, estimation theory and hypothesis testing. The exponential family of distributions. Regression models: simple and multiple linear regression, ANOVA, logistic regression and classification, LASSO, ridge regression Model selecion: Step-down, step-up methods, AIC, BIC, crossvalidation Additional topics: Modern high dimensional models (e.g. Matrix completion, sparse Gaussian graphical models), nonparametric models (density estimation and regression). Exchange/course-load context: The official incoming exchange catalogue states that 30xxx codes refer to undergraduate courses, 20xxx and 21xxx codes refer to graduate courses, and 50xxx codes refer to the Integrated Master of Arts in Law. Undergraduate exchange students are allowed to select undergraduate-level courses only; graduate students can choose both undergraduate and graduate level courses. Bocconi credits are ECTS-equivalent. Each Bocconi credit corresponds to 25 hours of workload, including 8 lecture hours.