ADVANCED STATISTICS FOR ECONOMICS AND SOCIAL SCIENCES

Description

The course is designed to provide an in-depth knowledge of the main aspects of statistical inference (point estimation and hypothesis testing), both from a conceptual and a technical point of view. Optimality principles are discussed for the main procedures, based on the properties of sufficiency, completeness, and ancillarity of statistics and based on the likelihood principle. The implications of such concepts are analyzed both within the finite sample case and in the asymptotic setting. Principles and techniques discussed in the course are relevant to the development and analysis of statistical models in many areas (e.g., in the linear model and its generalizations). Properties and results for random variables. Sufficient, ancillary, and complete statistics. Point estimation: method of moments and method of maximum likelihood. Comparison among estimators and optimality results (Mean Squared Error, Uniform Minimum Variance Estimators, Fisher’s information, Loss function). Hypothesis testing: criteria and construction of optimal tests within the Neyman-Pearson framework (power of tests). Tests based on the likelihood ratio. The role of the p-value and of tests of significance. Asymptotic considerations: consistent and asymptotically efficient estimators. Likelihood-based asymptotic tests and confidence intervals. Introduction to Bayesian inference and comparison to the classical framework. 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.