| Area of Mathematics: | Statistics-Probability-Operational Research (ESPOR) | ||
| Semester: | 6ο | ||
| Course ID: | 62301 | ||
| Course Type: | Elective | ||
| Teaching hours per week: | Theory: 3 | Practice: 1 | Laboratory: 0 |
| ECTS : | 5 | ||
| Eclass: | For the course’s material, click here. |
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| Instructors: | |||
Description
- The notions of statistical hypothesis and statistical test. Type I error, type II error, power of a test. P-value of a test.
- Relation between tests and confidence intervals.
- Fundamental Lemma of Neyman-Pearson. Uniformly most powerful (UMP) tests. Monotone likelihood ratio property and UMP test for one parameter exponential families. Applications to normal populations.
- Generalized likelihood ratio tests. Z-test, t-test (for one or two normal populations), Chi-square test and F test. Chi-square goodness of fit test, test of independence in contingency tables.
- Empirical distribution function and Kolmogorov-Smirnov test for one or two populations.
- Bayes tests and minimax tests.
Bibliography
- Hogg R.V., McKean J.W., Craig A.T., Introduction to Mathematical Statistics, 8th ed., Pearson, 2018
- Casella G., Berger R.L., Statistical Inference, 2nd ed., Duxbury Press, 2002
- Lehmann E.L., Romano J.P., Testing Statistical Hypotheses, 3rd ed., Springer, 2005
