Mathematical Statistics 2400-PP2STa
1. Introduction: paradigm of Mathematical Staistics; mathematical models and empirical
inference.
2. Probability distributions and their empirical counterparts
3. Statistical models: families of probability distributions, parametric and nonparametric
models
4. Methods of estimation: the method of moments, maximum likelihood
5. Properties of estimators: bias, mean square error, Mimimum variance unbiased estimators,
Cramer-Rao inequality
6. Confidence intervals
7. Testing statistical hypotheses: test of significance, Neyman-Pearson lemma, most powerful
tests, typical parametric
and nonparametric tests
8.Selected special topics: e.g. Bayesian approach or introduction to multivariate analysis
Type of course
Course coordinators
Learning outcomes
KNOWLEDGE
The student knows and understands selected concepts of probability calculus and mathematical statistics, the most important of which is a random variable, distribution of a random variable, basic characteristics of the distribution of a random variable and types of random variables. Knows the theory of statistical inference, point estimation, interval estimation, the theory of verification of statistical hypotheses. The student knows parametric and nonparametric models for verification of hypotheses regarding theoretical distribution.
SKILLS
The student is able to use the tools of mathematical statistics. He can use selected statistical procedures. Student is able to describe models in formal statistical language. The student is able to use analytical methods to correctly formulate and solve tasks in the field of mathematical statistics. The student is able to construct an unbiased and effective parameter estimator using the chosen method. The student is able to estimate the parameter using the confidence interval. He can verify the hypothesis regarding theoretical distribution.
COMMON SKILLS
The student knows the applications of theories and methods of mathematical statistics in economics and related sciences
Assessment criteria
Discussions assessment: The class grade is based on the sum of points obtained from: two tests (max 30 points each), online moodle activity/quizzes (max 20 points) and class activity (max 20 points). A student needs to have at least 50 points and at most two absences to pass classes.
Lecture assessment: the final grade is based on the weighted average: 1/3 class grade + 2/3 final exam grade, with the final exam grade based on the results of an exam consisting of 8 problems to solve (worth 2 points each). In order to obtain a passing final grade, the weighted average needs to be equal to at least 2.5, with the exam score equal to at least 6.5 points.
Bibliography
1. Michel Lavine, Statistical Thought, available online:
www.stat.duke.edu/~michael/book.html
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: