
 derive, use and analyse, including the convergence properties thereof, different standard estimators in statistics;
 explain and interpret, properly, the use of confidence intervals in statistical data analysis


Modelling real life phenomena often involves probabilistic modelling of unknown quantities. The part Mathematical Statistics builds further on Probability Theory of Module04AM (“Signals and Uncertainty”). Whether consciously or not, we come across statistics in our everyday life: from an opinion poll to a forecast of stock market behaviour in the future. Often, we see statements like: "There is 52% support for the current proposal with 4% margin of error" or “The result is statistically significant”. What do they actually mean? What is the use of, for example, knowing the estimated yield, say 4%, from a certain financial portfolio, if the performance of the past does not guarantee that in the future? In Mathematical Statistics, ample attention will be given to the mathematical theories that lie underneath the statements like these and thereby the proper interpretations thereof. Several standard estimators, for different probabilistic models, will be discussed and compared. How much can an estimator deviate from the true value? Confidence intervals give an answer to that. Does a dietprogramme really work? To answer the question statistically, one needs the theory of hypothesis testing. Theory of regression analysis, on the other hand, is essential in exploring the relationship between different variables. Besides the mathematics behind these theories, you will also learn how to apply them appropriately in different situations such as with normal and binomial populations (parametric methods), categorical variables, and more general populations (nonparametric methods).
Assessment
The grade for Mathematical Statistics is determined by the statistics test and a few homework assignments.




 Assumed previous knowledgeKnowledge of probability theory as thought in the course Probability Theory Module 4) is required. 
Bachelor Applied Mathematics 
  Required materialsReaderLecture Notes: Mathematical Statistics with applications (Meijer and Poortema) 

 Recommended materialsBookViktor Panaretos “Statistics for Mathematicians: A Rigorous First Course” (Compact Textbooks in Mathematics) 

 Instructional modesTestsMathematical Statistics


 