MATHEMATICAL STATISTICS

The main goal of the course is to provide the basic aspects of statistical inference (mainly for i.i.d. data) for both non-parametric and parametric models.

An elementary course in probability and statistical inference. Basic notions of measure theory and Lebesgue integration would be useful, although not strictly necessary.

Learning and use of basic methodologies of statistical inference at an intermediate level, for both parametric and nonparametric models. Applying knowledge of statistical inference techniques to problems in Economics and Econometrics. Making judgments: ability in collecting, using and critically interpreting data related to Economics and Finance. Ability in appropriately model such data, and in studying the chosen statistical models through statistical inference techniques. Communication skills: effective communication skills of statistical models construction and analysis. Learning skills: ability to learn autonomously statistical inference techniques.

Theoretical lectures on some basic aspects of probability theory, with particular reference to limit results (Laws of Large Numbers and Central Limit Theorems). Main Statistics used in nonparametric statistics: empirical distribution function, order statistics, sample quantiles. Statistical functionals: consistency and asymptotic normality. Estimation of asymptotic variance. resampling techniques, with special emphasis on nonparametric bootstrap and jackknife. Introduction to smoothing. Esercizi (teorici e pratici) sugli argomenti studiati nella teoria.

R.J. Serfling: “Approximation Theorems of Mathematical Statistics” Ed. Wiley. L. Wasserman: “All of Nonparametric Statistics” Ed. Springer. Lectures notes