# Syllabus

### I. Course description:

Statistical methods, based on the assumption that the data generating process involves random components, are pervasive in modern quantitative data analysis. A rigorous foundation in the principles of probability and mathematical statistics underlying statistical analysis is therefore essential to data-based approaches, (not only) in the field of economics and business.

This semester, special emphasis is given to the probability foundations of statistical analyses; among others, we shall study parametric families of distributions, univariate as well as multivariate.

The course is a prerequisite for the Advanced Statistics II class focusing on inferential statistics, where we discuss methods of statistical inference, in particular parameter estimation and hypothesis testing. As such, it provides the foundation for specialization courses in statistics and econometrics (like Time Series Analysis, Statistics for Financial Markets, Econometrics, Multivariate Statistics, etc.).

### II. Prerequisities:

Calculus (no excuses!), some algebra.

### III. Method of Assessment:

Written exam (online)

1. ### Elements of Probability Theory

2. Random Variables and their Probability Distributions
3. Moments of Random Variables
4. Parametric Families of Density Functions
5. Basic Asymptotics

V. Materials:

• Lecture notes (OLAT)
• Slides and videos will be made available in due time (OLAT again)
• Main textbooks:
- Mittelhammber, R.C. (1996). Mathematical Statistics for Economics and Business. Springer.
- Mood, A. M., F.A. Graybill and D.C. Boes (1974, 3rd ed.). Introduction to the Theory of Statistics. McGraw-Hill.

Other useful ones (by far not an exhaustive list)

• Casella, G. and R. Berger (2002, 2nd ed.). Statistical Inference. Duxbury.
• Wassermann, L. (2004). All of Statistics: A Concise Course in Statistical Inference. Springer.
• Rohatgi, V.K. und A.K. Saleh (2001, 2nd ed.). An Introduction to Probability Theory and Mathematical Statistics. John Wiley & Sons.
•  Linton, O. (2017). Probability, Statistics and Econometrics. Academic Press.

VI. Schedule:

•  course, 2 hrs. per week; there will be new videos each week, and the original time
slot is used for live Q&A (BigBlueButton)
• pen&paper tutorial, 2 hrs. per week (live online); you have the choice between three different time slots
• non-compulsory computer class: 2 hrs. every
second week (live online and/or videos)
• see univis for exact times of the live sessions!