2013000087.5 ECTSEnglishMaster
Fundamentals of statistics
Faculteit—
NiveauMaster
Studiejaar2026-2027
Beschrijving
Course goals
TESTING AND COURSE AIMS
In this course, two exams are administered.
The exams are used to test knowledge of the topics discussed and the ability to solve mathematical statistics problems. The grade for each test counts for 40% of the final grade. In addition, there will be an assignment each regular week. Students can work on the assignments together but the work should be handed in individually. At least four of the assignments will be graded. The assignments that will be graded, are randomly selected.
The mean of the grades for the assignments counts for 20% of the final grade.The final grade must be at least 5.5.
The mean of the grades for the assignments counts for 20% of the final grade.The final grade must be at least 5.5.
At the end of the course students are supposed to have knowledge of:
- the central limit theorem;
- properties of estimators, such as unbiasedness, efficiency, sufficiency, consistency and robustness;
- the Neyman-Pearson lemma.
In addition, students should be able:
- to solve several calculus problems;
- to work with matrices;
- to apply several rules of probability;
- to work with multivariate, conditional and marginal distributions;
- to select different probability distributions and densities;
- to derive the moments of a distribution or density by means of the moment generating function;
- to determine the moments of linear combinations of random variables;
- to apply the method of least squares, the method of moments, the method of maximum likelihood, and Bayes estimation;
- to apply small sample techniques in hypothesis testing; to construct likelihood ratio tests
Content
This course provides an introduction to mathematical statistics that is relevant to empirical research.
The main topics are: mathematical requirements (differentiation, integration, numerical procedures), counting techniques, probability theory, general properties of probability distributions and densities, special probability distributions and densities, expectation, moments, sampling theory, point estimation (properties of estimators, method of moments, least squares estimation, maximum likelihood estimation, Bayesian estimation), hypothesis testing theory and applications (small sample techniques, likelihood ratio test, Wald test), analysis of variance, and regression.
The main topics are: mathematical requirements (differentiation, integration, numerical procedures), counting techniques, probability theory, general properties of probability distributions and densities, special probability distributions and densities, expectation, moments, sampling theory, point estimation (properties of estimators, method of moments, least squares estimation, maximum likelihood estimation, Bayesian estimation), hypothesis testing theory and applications (small sample techniques, likelihood ratio test, Wald test), analysis of variance, and regression.
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