## 10592625 - Advanced statistics for finance 2022/2023

Students should join the course using Google Classroom (code: sdsjueo). Materials and announcements about the course will be posted exclusively on Google Classroom.

Schedule (Orario lezioni)

• Tuesday 10-12 (room: Sala Pescatore)
• Wednesday 10-12 (room: Sala Pescatore)

Language (Lingua)

English

The final grade will be based on a written exam with a theoretical component (which will weigh 70% of the final grade) and a practical application (which will weigh 30% of the final grade). The former will require solving theoretical problems. The latter will require elaborating and interpreting the output from an R data analysis.

The calendar of the exam sessions is available on the course webpage from the courses catalogue.

Teaching delivery modality (Modalità di svolgimento)

Classes will be in-person and will take place as scheduled.

Prerequisites (Prerequisiti)

Essential prerequisites: basic (mean, variance, chi-square test, linear correlation) and intermediate (probability, random variables, linear regression) statistics; calculus (limits, integrals, derivatives).

Topics (Programma)

The content of the course will consist of the following topics, where the numbering reflects their temporal sequence. The number of hours is approximate and it includes computer lab.

1. Joint, marginal, and conditional distributions; likelihood; exponential families (6 hours)
2. Quantiles, order statistics and their sampling distributions; probability integral transform and pseudo-random sampling; random variables transformations (6 hours)
3. Introduction to statistical inference and modelling (parametric, non-parametric, and semi-parametric methods); introduction to computational statistics (e.g., Newton, Nelder-Mead, bootstrap) (8 hours)
4. Likelihood: definition, score function, Fisher information, maximum likelihood estimator and its properties, delta method univariate and multivariate (10 hours)
5. Generalized linear models: canonical representation; maximum likelihood estimation; optimization (iteratively reweighted least squares); linear, binomial (logit, probit, cloglog), and Poisson regression; multinomial regression; model selection (likelihood ratio test, Akaike information criterion) (14 hours)
6. Power analysis for regression analysis (4 hours)

Bibliography (Bibliografia di riferimento)

• Course slides
• Mood, Graybill, Boes. Introduction to the theory of statistics. McGraw-Hill
• Piccolo. Statistica. Il Mulino
• Cox and Hinkley. Theoretical statistics. Chapman and Hall
• Fahrmeir, Kneib, Lang, and Marx. Regression: Models, Methods, and Applications. Springer
• Crawley. The R book. Wiley
• Venables, Smith, and the R Core Team. An introduction to R. Available at: https://cran.r-project.org/manuals.html

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