Statistics

The course deals with statistical model-building and statistical inference.

Prerequisites
The students will be assumed to have learned, in previous classes, the following concepts of probability theory and descriptive statistics.
Students in need to refresh their quantitative background are advised to sit in the course Introduction to Statistics (master in Banking and Finance).
On the website of the course there are also lecture notes to review the topics mentioned below that are a pre-requisite for the course.

Probability Theory
Introduction to probability: definitions, concept of marginal and joint probability, low of total probability, conditional probability, notion of independence.
Random variables: discrete (Bernoulli, Binomial, Geometric, Poisson, Uniform), continuous (Uniform, Gaussian or Normal, Exponential, Student-T, Chi-square).
Central limit theorem and Law of large numbers.

Descriptive Statistics
Univariate: measure of location (mean, median, mode) and dispersion (variance, std deviation, quantiles).
Bivariate: two way tables, joint and marginal distributions, covariance and correlation. 
Graphical instruments to visualize data.

Details of the course
The course focuses on inferential statistics based on the concept of likelihood function.

Main topics
- Advance probability theory: exponential family of distributions
- Likelihood concept, both univariate and multivariate: Definition and main properties of the likelihood function.
- Parametric estimation; various principles for generating estimators (focusing on the maximum likelihood principle) and their properties (finite sample and asymptotic properties).

Main references
Lecture notes will be available on the e-learning website.
G. Casella and R.L. Berger, Statistical Inference, Pacific Grove, 1990.

Further references
E.L. Lehmann and G. Casella, Theory of point estimation, second edition, Springer, 1998.
A.M. Mood, F.A. Graybill, D.C. Boes, Introduction to the theory of statistics, 3. ed. - McGraw-Hill, New York, 1974 (also available in Italian).