Mathematical Statistics 2400-FIM2SM
The course consists of lectures and discussions. The discussions will be devoted to solving practical problems related to theoretical issues introduced during lectures. The topics covered include
Lectures 1,2:
1. Introduction to statistics and statistical concepts (population, characteristic etc.). Basic population characteristics (empirical CDF, mean, median, variance and other measures of location and dispersion).
2. Graphical presentation of data.
3. Statistical indices.
Lecture 3:
4. The statistical model and statistical inference. Concepts of estimation, hypothesis testing and prediction. The notion of a statistic. Basic probability distributions commonly used in statistics.
Lecture 4:
5. Point estimation (method of moments, quantiles, maximum likelihood).
Lectures 5,6,7:
6. Estimator properties: bias, measures of the quality of an estimator, estimator risk, information inequality, estimator efficiency.
7. Asymptotic estimator properties (consistency, asymptotic normality, asymptotic efficiency).
Lecture 8:
8. Interval estimation: confidence intervals for the parameters in a normal model, two-point distribution model, asymptotic confidence intervals.
Lecture 9:
9. Verification of statistical hypotheses. Notions of hypothesis, test, critical region, error of 1st and 2nd type, level of significance, p-value.
Lecture 10:
10. Test power, most powerful tests, Neyman-Pearson Lemma.
Lecture 11:
11. Tests based on likelihood ratio. Testing hypotheses about the parameters of a normal model. Comparing populations.
Lecture 12:
12. Comparing more than two populations (ANOVA). Asymptotic properties of the likelihood ratio tests.
Lecture 13:
13. Tests of consistency and independence. Kolmogorov tests, the chi-square test.
Lectures 14, 15:
14. The Bayesian model and Bayesian statistics. Prior and posterior distributions. The Bayesian estimator.
15. Summary.
Type of course
Prerequisites (description)
Course coordinators
Learning outcomes
Upon the completion of the course, the student:
-- knows the foundations of statistical inference theories, knows and understands the basic concepts (such as estimator, hypothesis, test, etc.) and standard methods of descriptive statistics (calculation of characteristics and data presentation) and mathematical statistics (estimation procedures, hypothesis testing procedures). The student knows and understands the methods of calculation and interpretation of basic statistical measures
-- the Student is able to construct a statistical model. The student is able to utilize analytical methods to formulate and solve basic statistical problems of descriptive statistics and mathematical statistics (for example, apply a suitable method of estimation). The student is able to plan and conduct a statistical experiment, formulate hypotheses, interpret the results and derive conclusions. The student is able to apply basic methods of statistical inference.
-- The student is aware of the necessity to verify economic theories statistically, on the base of empirical data. The student is aware of the fact that the set of analytical tools which may be used for hypothesis verification is constantly widening.
KU04, KW01
Assessment criteria
Discussions assessment: The class grade is based on the sum of points obtained from: three tests (max 20 points each), homework assignments (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 online exam. The exam will consist of 8 problems to solve; the answers will need to be marked in an online test and scans of problem solutions will need to be submitted.
Bibliography
Dennis Wackerly, William Mendenhall, Richard L. Scheaffer , Mathematical Statistics with Applications, Duxbury Press
Michel Lavine, Statistical Thought, available online:
www.stat.duke.edu/~michael/book.html
Lecture notes (to be distributed)
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: