Course Code : | 1001WETWST |

Study domain: | Mathematics |

Academic year: | 2019-2020 |

Semester: | 2nd semester |

Sequentiality: | Minimum 8/20 Kanstheorie en parallel opnemen van Maattheorie EN alle vakken Ba1 Wis min 8/20 |

Contact hours: | 60 |

Credits: | 6 |

Study load (hours): | 168 |

Contract restrictions: | No contract restriction |

Language of instruction: | Dutch |

Exam period: | exam in the 2nd semester |

Lecturer(s) | Tim Verdonck |

At the start of this course the student should have acquired the following competences:

an active knowledge of

an active knowledge of

- Dutch

Knowledge of basic concepts of probability theory: random variable, distribution, density, characteristic function, expectation, covariance, covariance matrix, notions of convergence ...: univariate as well as multivariate.

Knowledge of basic concepts and notations of measure theory.

Students are able to work with classical well known distributions. For a generally defined distribution they can compute and interpret typical properties such as expectation, etc.

- you can find an estimator for an unknown parameter of a given parametric model and check the main properties of this estimator ;
- you can assess the quality of an estimator and compare an estimator with other estimators ;
- you can conduct inference concerning the parameter of a specific 1-parametric model, i.e. construct a confidence interval and perform hypothesis tests ;
- you can identify which hypothesis test should be used given a concrete situation and you can perform this test and draw an appropriate conclusion ;
- you can fit an appropriate linear model given a specific situation and you are aware of the model assumptions and know how to check them ;
- you can perform hypothesis tests concerning linear models to answer specific questions (e.g. is there a significant difference between several groups; are two variables connected; ...) ;
- you have a good knowledge of R to apply all aforementioned methods on concrete data sets. You can draw correct conclusions based on R output.

- We define the basic concepts of statistical models: statistical models, likelihood function, parametric model, non-parametric model, random sample, empirical distribution, …
- We define the basic concepts of statistics: statistic, image space, sufficient statistic, complete statistic, minimal sufficient statistic, … and we discuss various examples of widely used statistics (sample mean, sample variance, order statistics, rank statistics, …)
- We discuss parameter estimation within a parametric model: we study methods to find an estimator and to check its properties.
- We discuss the construction of a confidence interval for an unknown parameter.
- We study the mechanism of hypothesis tests about a parameter. We introduce some specific hypothesis tests and we discuss which test is most appropriate under which circumstances.
- We introduce the linear model. We discuss parameter estimation and the construction of confidence intervals and hypothesis tests.
- We use the statistical software package R to apply a data analysis based on statistical methods.

Class contact teachingLectures Practice sessions Laboratory sessions

Personal workExercises

Personal work

Written assignment

Examination

Written assignment

Course notes and slides are available through blackboard.

Mathematical Statistics and Data Analysis - J.A. Rice

Introduction to mathematical statistics - L.Schmetterer

Mathematical statistics - J. Shao

Mathematical Statistics with Applications - D. Wackerly, W.Mendenhall and R.L. Scheaffer

Professor: Tim Verdonck (Tim.Verdonck@uantwerpen.be)