| TAMS17 |
Statistical theory, advanced course, 6 ECTS credits.
/Statistisk teori, fortsättningskurs/
For:
Mat
MMAT
Y
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Prel. scheduled
hours:
Rec. self-study hours: 160
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): A
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Aim:
The course gives an introduction to the general
theory of statistical inference. After a completed course the student is expected to be able to:
- describe advanced concepts and theorems of theoretical
statistics, e.g., sufficiency, completeness, and the Neyman-Pearson lemma, and to prove some of the theorems.
- construct suitable, in some cases optimal, point estimators,
hypothesis tests, and confidence sets, in general situations where the
data are observations from a parametric family of probability distributions.
- carry out Bayesian inference in general situations where the
data are observations from a parametric family of probability distributions.
- derive asymptotic results for point estimators, hypothesis tests, and confidence sets.
- understand and assess statistical inference occurring in
other undergraduate courses, research reports, or the media.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Basic courses in probability theory and
statistics. An advanced course in probability theory is helpful, but
not required.
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Organisation:
Lectures and tutorials.
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Course contents:
Exponential families. Location and scale
families. Sufficient, mimimal sufficient, ancillary, and complete
statistics. Methods for point estimation, e.g. maximum likelihood.
Evaluation of point estimates using e.g. the Cramer-Rao inequality and
the Rao-Blackwell theorem. Likelihood ratio tests. Uniformly most
powerful tests and the Neyman-Pearson lemma. The correspondence
between tests and confidence sets. Pivotal variables. Optimality for confidence sets.
Bayesian inference and decision theory. Asymptotic theory.
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Course literature:
Casella, G., Berger, R.L., Statistical Inference. Duxbury Press.
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Examination: |
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Written examination
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6 ECTS
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Course language is Swedish/English.
Department offering the course: MAI.
Director of Studies: Ingegerd Skoglund
Examiner: Torkel Erhardsson
Link to the course homepage at the department
Course Syllabus in Swedish
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