Courses Exchange Display 20222023
Course Description  To PDF  

Course title  Mathematical Statistics  
Course code  EBC2107  
ECTS credits  6,5  
Assessment  Whole/Half Grades  
Period 


Level  Intermediate  
Coordinator 
Stephan Smeekes For more information: s.smeekes@maastrichtuniversity.nl 

Language of instruction  English  
Goals 
Understanding of statistical principles: population models and sampling processes; sampling theory in small samples and in large samples.
Understanding of main methods of statistical inference: point estimation, hypothesis testing, interval estimation. Working knowledge of linear regression models and bootstrap methods. Some applications of statistical models and methods to practical problem solving. 

Description 
PLEASE NOTE THAT THE INFORMATION ABOUT THE TEACHING AND ASSESSMENT METHOD(S) USED IN THIS COURSE IS WITH RESERVATION. A REEMERGENCE OF THE CORONAVIRUS AND NEW COUNTERMEASURES BY THE DUTCH GOVERNMENT MIGHT FORCE COORDINATORS TO CHANGE THE TEACHING AND ASSESSMENT METHODS USED. THE MOST UPTODATE INFORMATION ABOUT THE TEACHING/ASSESSMENT METHOD(S) WILL BE AVAILABLE IN THE COURSE SYLLABUS.
Mathematical Statistics is a sequel to the firstyear Probability Theory course. Here we utilise the formal tools of probability distributions to introduce you to the principles of statistical inference. Whereas probability theory can be seen as a branch of deductive mathematics, statistical inference proceeds by inductive reasoning. What this means, in a nutshell, is that general conclusions about entire populations (the "real world") are based on relatively small samples extracted from it (the "data"). It is impossible to make such generalisations without some risk of being wrong. Indeed, much of the “mathematical” content of statistics serves precisely to evaluate and control that risk. The subject matter covered in the course includes random samples and sampling distributions, methods of point estimation, interval estimation and hypothesis testing, the evaluation of these methods in small and large samples, and some applications, with an emphasis on simple linear regression and the bootstrap. 

Literature 
Casella G. & R.L. Berger, Statistical Inference, 2nd edition, Duxbury Press, Thomson Learning, 2002. ISBN 0534243126. Chapters 611, the first five chapters of this same textbook were covered in the preceding Probability Theory course. Additionally, lecture notes on the bootstrap (distributed via the course website).


Prerequisites 
Algebra, calculus, mathematical analysis, set theory, and probability theory.
ATTENTION: This course is NOT introductory. The material studied in this course relies very heavily on the material from Chapters 1 through 5 of Casella & Berger (2002). These chapters are assumed to have been studied before the course and are therefore not discussed during the course. A thorough prior knowledge of probability theory on the level of Chapters 1 through 5 of Casella & Berger (2002) is therefore required for this course. Basic knowledge of probability theory through an introductory course is not sufficient. 

Teaching methods (indicative; course manual is definitive)  Lecture / Assignment / Groupwork  
Assessment methods (indicative; course manual is definitive)  Final Paper / Participation / Written Exam  
Evaluation in previous academic year  For the complete evaluation of this course please click "here"  
This course belongs to the following programmes / specialisations 
