20137 - ADVANCED STATISTICS FOR ECONOMICS AND SOCIAL SCIENCES

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.

• Understand the key guiding principles and concepts of statistical inference.
• Master intermediate statistical and probabilistic tools.
• Identify drawbacks and merits of different estimation procedures.
• Profitably attend courses on advanced topics in Probability and Stochastic Processes, Statistics and Machine Learning, Econometrics.

• Formulate a suitable probabilistic model to analyze the random phenomenon under investigation.
• Apply appropriate and, if possible optimal, statistical methodology to point estimation problems.
• Address hypothesis testing problems in a principled way.
• Interpret the outcome of the estimation procedure in view of the application at hand.

• Face-to-face lectures

Face-to-face lectures.

• A written general exam or two partial written exams (one in the middle and one at the end of the course).
• The exam consists of: (a) excercises to ascertain the ability to formulate a model and to derive the key statistical properties; (b) open answer questions to assess the understanding of the theoretical aspects. 
• There are no different assessment method/exam program between attending and non attending students.

• N. MUKHOPADHYAY, Probability and Statistical Inference, Dekker-CRC Press, 2000.
• G. CASELLA, R.L. BERGER, Statistical Inference, 2nd Ed., Duxbury, 2002 (as additional reference).
• Additional materials as posted on the web learning space of the course.