# Mathematical Statistics

Course Code : | 1001WETWST |

Study domain: | Mathematics |

Academic year: | 2017-2018 |

Semester: | 2nd semester |

Sequentiality: | - |

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) | ValĂ©rie De Witte |

### 1. Prerequisites *

specific prerequisites for this course

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.

### 2. Learning outcomes *

- 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.

### 3. Course contents *

- We define the basic concepts of statistical models: statistical models, likelihood function, parametric model, non-parametric model, random sample, empirical distribution, … (Chapter 1)
- 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, …) (Chapter 2)
- We discuss parameter estimation within a parametric model: we study methods to find an estimator and to check its properties (Chapter 3).
- We discuss the construction of a confidence interval for an unknown parameter (Chapter 4).
- 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 (Chapter 5).
- We introduce the linear model. We discuss parameter estimation and the construction of confidence intervals and hypothesis tests (Chapter 6).
- We use the statistical software package R to apply all statistical methods.

### 4 International dimension*

The course has an international dimension.

### 5. Teaching method and planned learning activities

Personal work

### 6. Assessment method and criteria

Written assignment

Examination

Written assignment

### 7. Study material *

#### 7.1 Required reading

Course notes and transparencies are available through blackboard.

**7.2 Optional reading**

The following study material can be studied voluntarily :Introduction to mathematical statistics - L.Schmetterer

Mathematical statistics - J. Shao

### 8. Contact information *

Lecturer: Florence Guillaume (Florence.Guillaume@uantwerpen.be)

Assistant: Valérie De Witte (Valerie.DeWitte@uantwerpen.be)