Statistical functions: Sample Distributions. Sufficiency, completeness, efficiency, and consistency. Exponential families of distributions. Estimators: Unbiasedness. Unbiased estimators of minimum variance and their construction. Rao–Blackwell Theorem. Fisher Information. Cramer-Rao Inequality. Methods of estimator construction: Method of moments, maximum likelihood method, and Bayesian estimation. Asymptotic properties of estimators. Construction of confidence intervals. Hypothesis testing: Likelihood ratio tests, Wald tests, score tests. Linear Regression: Simple and general linear regression. Analysis of variance: One-way and two-way analysis of variance.
- Teacher: Δημήτριος Φουσκάκης
ECTS : 6
Language : el
Learning Outcomes : Upon successful completion of the course, the student will be able to:
• Understand the basic principles of estimation theory, the main criteria for choosing estimators, the methods for calculating them, and the techniques for constructing estimators. In addition, they will understand the concept and necessity of Confidence Intervals and how they are constructed. Finally, they will understand the fundamental ideas of hypothesis testing and the methods for constructing “optimal” critical regions.
• Understand how, from a mathematical perspective, we extract information obtained from a sample in order to generalize it to the entire population, using Probability models.
• Compute appropriate quantities in order to answer the given research question and evaluate their results.