# Statistical Inference (MAE633)

### General

School School of Science Department of Mathematics Undergraduate ΜΑΕ633 6 Statistical Inference Lectures (Weekly Teaching Hours: 3, Credits: 6) Special Background - Greek Yes (in English, reading Course) See eCourse, the Learning Management System maintained by the University of Ioannina.

### Learning Outcomes

Learning outcomes The aim of the course is to present and study techniques and methods of parametric statistical inference. In particular, the interest is mainly focused on the theoretical development of the field of parameter estimation (point and interval) and the development of the theory of statistical tests for testing statistical hypotheses. Moreover, this course aims to provide the necessary tools and methods which help students to be able to draw statistical conclusions on the basis of experimental data and by utilizing these methods. At the end of the course students will have acquired the theoretical background of the parametric statistical inference methodologies. Working independently Decision-making Production of free, creative and inductive thinking Criticism and self-criticism.

### Syllabus

Point estimation: unbiased, sufficient and efficient estimators, unbiased estimators with minimum variance, the Cramer-Rao lower bound for the variance, Lehmann-Scheffe theory, asymptotic properties of estimators, methods of estimation (method of maximum likelihood and method of moments). Interval estimation. Confidence intervals. Testing Statistical Hypothesis: the Neyman- Pearson lemma, simple and composite hypotheses, uniformly most powerful tests, likelihood ratio tests. Large sample tests. Applications.

### Teaching and Learning Methods - Evaluation

Delivery

Classroom (face-to-face)

Use of Information and Communications Technology Use of ICT in communication with students
Teaching Methods
Lectures 39
Working independently 78
Exercises-Homeworks 33
Course total 150
Student Performance Evaluation

Final written exam in Greek (in case of Erasmus students in English) which concentrates on the solution of problems which are motivated by the main themes of the course.

### Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

• Casella, G. and Berger, R. (2002). Statistical Inference. 2 Edition. Duxbury Advanced Series.
• Hogg, R. V., McKean, J. W. and Craig, A. T. (2005). Introduction to Mathematical Statistics. Pearson Education, Inc.
• Mood, A., Graybill, F. and Boes, D. (1974). Introduction to the Theory of Statistics. McGrawHill.
• Roussas, G. (2003). An Introduction to Probability and Statistical Inference. Academic Press.
• Κουρούκλης, Σ. (2007). Στατιστική Ι. Πανεπιστήμιο Πατρών.