Mathematical Statistics

fakultatywne

Course objectives: By the end of the course the student should have developed the skills to: verify when statistics are sufficient (minimum syfficient); determining the loss function; apply statistical decision theory in testing hypotheses. Also know: the advantages and disadvantages of different classes of estimators; how to termine the estimators in the class; properties of exponential statistical spaces and statistics in these spaces.

Course profile: academic

Form of study: stationary

Course type: obligatory

Academic discipline: science and natural science, field of study in the arts and science: mathematics

Year: 2, semester: 3

Prerequisities:

lecture 30 h. exercise class 30 h.

Verification methods: lectures, exercises, consultations, studying literature, home works, discussions in groups.

ECTS credits: 5

Balance of student workload:

attending lectures15x2h = 30h

attending exercise classes 15x2h = 30h

preparation for classes 7x3h = 21h

completing notes after exercises and lectures 7x2h = 14h

consultations 12x1h = 12h

the final examination: preparation.and take 12h + 3h = 15h

control works: repeating the material and preparation 3x4h = 12h

Quantitative description

Direct interaction with the teacher: 75 h., 3 ECTS

1. Shao J., Mathematical Statistics: Exercises and Solutions, Springer 2005.

2. Shao J., Mathematical Statistics, Springer Texts in Statistics, Springer 2003.

3. J. R. Barra, Mathematical Basis of Statistics (Probability & Mathematical Statistics), Academic Press Inc. 1981

4. J. Devore, K. Berg, Modern Mathematical Statistics with Applications, Springer Texts in Statistics , 2012

Learning outcomes:

Students know the major theorems of mathematical statistics related to statistical spaces, statistics, exponential statistical spaces, hypothesis testing, theory of estimations, decision theory - KA7_WG03.

Students know how to use R/SPSS software for statistical processing of data - KA7_WG07, KA7_WK03, KA7_UW01.

Students know foundations of the theory of Fisher information - KA7_WG09.

Students understand fundamentals of mathematical statistics and statistical processing of data bases - KA7_UW12.

Students are able to determine the statistics and estimators with selected properties, as well as to test hypotheses - KA7_UW12.

Be able to express in writing and oral statistical content - KA7_UK02.

The overall form of credit for the course: final exam.