Study-unit PROBABILITY AND STATISTICS II - MATHEMATICAL STATISTICS
| Course name | Mathematics |
|---|---|
| Study-unit Code | A002327 |
| Curriculum | Didattico-generale |
| Lecturer | Andrea Capotorti |
| Lecturers |
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| Hours |
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| CFU | 6 |
| Course Regulation | Coorte 2023 |
| Supplied | 2023/24 |
| Supplied other course regulation | |
| Learning activities | Affine/integrativa |
| Area | Attività formative affini o integrative |
| Sector | MAT/06 |
| Type of study-unit | Opzionale (Optional) |
| Type of learning activities | Attività formativa monodisciplinare |
| Language of instruction | Italian |
| Contents | Sufficiency and likelihood principles. Bayesian and non-Bayesian parameter estimators: detection and properties. Theretical aspects of hypothesis testing. |
| Reference texts | G. Casella, R.L. Berger, Statistical Inference, second edition, Thomson Learning, 2002. |
| Educational objectives | Deep knowledge of statistical mathematical principles, both Bayesian and not.Students will be able to face and solve theoretical problems about parameter estimation, hypothesis testing and analysis of variance. They will be also able to consciously express the learned notions. |
| Prerequisites | To be able to understand the course and to pass the examination are mandatory the formative goals of the course Probability and Statistic I |
| Teaching methods | Lectures on all the subjects and public resolution of exercises to train students to face explicit problems and to explain them. |
| Other information | For students with Specific Learning Disorders and/or Disabilities please refer to the web page: http://www.unipg.it/disabilita-e-dsa |
| Learning verification modality | Written (with possibility of partial intermediate testing during lectures) of two exercises apt to verify ability in facing explicit problems and oral examination of around half an hour apt to verify the study on all the subjects and the ability in explaining and manipulate the studied notions. The result of the written test is not binding to access the oral test but constitutes the starting point and has a weight of about 1/4 on the final result. |
| Extended program | Transformation of random variables: monotonic and generic transformations; integral probability transformation; order statistics; conditional expexted value and variance.Sufficient and Likelihood Principles: sufficient principle; sufficient, minimal sufficient, ancillary and complete statistics; likelihood principle; MLE estimators and their invariance property.Finding and evaluating classical and Bayesian point estimators: moments method; unbiasedness; efficiency; Cramer-Rao lower bound; UMVUE estimators.Theoretical Deepening on Hypothesis Testing: LRT tests, power function. |