- Limit Theorems
- Estimation of Parameters and Fitting of Probability Distributions
- Testing Hypotheses and Assessing Goodness of Fit
- Comparing Two Samples
- The Analysis of Categorical Data
Language of instruction
|Thursday||03/04/21||09:00 AM - 01:00 PM||Online-Einheit|
|Thursday||03/11/21||09:00 AM - 01:00 PM||Online-Einheit|
|Thursday||03/18/21||09:00 AM - 01:00 PM||Online-Einheit|
|Thursday||03/25/21||09:00 AM - 01:00 PM||Online-Einheit|
|Thursday||04/15/21||09:00 AM - 01:00 PM||Online-Einheit|
|Wednesday||04/21/21||02:00 PM - 04:00 PM||Online-Einheit|
|Thursday||04/22/21||09:00 AM - 01:00 PM||Online-Einheit|
|Monday||04/26/21||08:00 AM - 12:00 PM||Online-Einheit|
After completing this course the student will have the ability to:
- describe and apply the key methods of statistical inference;
- solve fundamental statistical inference problems both theoretically and empirically.
- demonstrate effective team skills in order to contribute appropriately to the production of a group output;
- work, communicate and participate effectively in a team situation and group discussions and to function as a valuable and cooperative team member.
Moreover, after completing this course the student will have the ability to:
- adequately communicate the results of fitting statistical models to data;
- discuss empirical findings in the light of domain knowledge.
In addition, the student will be able to:
- use R to perform statistical inference.
The course will be taught in distance mode, hence, compulsory attendance applies to all online units. This means that students should attend at least 80% of all lectures, at most one lecture can be missed.
The course is taught as a lecture combined with homework assignments and a course project.
In combination with the lecture, the homework assignments will help students to consolidate and expand their knowledge and understanding by developing solutions to theoretical and applied problems and have to be submitted every week via email to the lecturer.
For the course projects, teams with up to five members will cooperate in solving statistical inference problems using a mix of analytical and numerical computations and present their results for one such project.
* 40% home assignments and colloquia
* 30% course project
* 30% written final exam
The assessment of the homework assignments and course projects will be based on the correctness of results, the clarity, and persuasiveness of each bit of work, and the recognizable effort made. This implies an ability to work in teams.
For the written exam, the assessment will be based on the ability to describe and apply the key concepts discussed throughout the course and to choose the appropriate analytical techniques to obtain the relevant data.
To avoid the potential free-rider problem related to group work, the final exam will strongly be related to the problems already discussed in homework assignments and course projects.
- Advanced Business Mathematics (see the class Mathematics I of the QFin program)
- Advanced Business Probability theory (see the class Probability of the QFin program)
- Basic Statistical Computing (see the class Statistics I of the QFin program)
Limit Theorems; Basic Framework of Statistical Inference
After attending this session students should recall the basic concepts for and results about convergence of sequences of random variables, and the understand the basic framework of statistical inference.
Reference: Rice, Chapters 5 and 8.1-8.3.
Estimation of Parameters and Fitting of Probability Distributions
After attending this session students should understand the principles of fitting (families of) probability laws to data, in particular for situations where the family depends on a small number of parameters
Reference: Rice, Chapter 8.4-8.8.
Testing Hypotheses and Assessing Goodness of Fit
After attending this session students should be able to recall the Neyman-Pearson paradigm for statistical hypothesis testing, and the principles of assessing the goodness of fit of probabilistic models to data.
Reference: Rice, Chapter 9.
Comparing Two Samples
After attending this session students should be familiar with methods for comparing samples from (continuous) distributions that may be different, in particular methods for making inferences about how the distributions differ.
Reference: Rice, Chapter 11.
Analysis of Categorical Data
After attending this session students should be able to remember statistical inference techniques for categorical data and contingency tables, including tests for independence, homogeneity, and symmetry.
Reference: Rice, Chapter 13.
Presentations and Review
After attending this session students should recall developing, presenting and discussing the results of using a mix of analytical and numerical computations to solve statistical inference problems.