Opleiding: Probability Theory and Statistics 3

eerdoelen

The student obtains fundamental insights into classical mathematical statistics and is able to work with basic statistical models. Students will be able to:

• Demonstrate and apply various statistical convergence notions and including convergence in distribution;
• convergence in probability, stochastic convergence and asymptotic normality;
• evaluate and compare point estimators based on properties of these estimators (consistency, efficiency, relative efficiency);
• apply various methods for finding a 'uniform minimum variance unbiased estimator' (UMVUE) of a given parameter;
• work with the concepts 'completeness' and 'sufficiency' and understand the role of these concepts in deriving optimal estimators, confidence intervals and statistical hypothesis tests;
• use various techniques to derive confidence intervals and statistical tests;
• understand and derive elementary properties of tests such as the size and power of tests;
• command several ways to find uniform most powerful tests;
• derive and apply generalized likelihood ratio tests.

Inhoud

• Limiting distributions, convergence in distribution and degenerate limiting distributions.
• Central Limit Theorem.
• Asymptotic normality, convergence in probability and stochastic convergence.
• Properties of estimators and unbiasedness.
• Cramer-Rao lower bound.
• Uniform minimum variance unbiased estimators.
• Sufficiency.
• Factorisation criterion.
• Rao-Blackwell 'improvement' theorem.
• Lehmann-Scheffe.
• Completeness.
• Regular exponential class.
• Confidence intervals and pivotal quantities.
• Relation between tests and confidence intervals.
• Significance level.
• Simple/joint hypotheses.
• Neyman-Pearson lemma.
• Uniformly most powerful tests.
• Generalised likelihood ratio tests.

Aanbevolen voorkennis

Probability Theory and Statistics 2 is highly recommended.

Werkvorm

Weekly two two-hour lectures and one three-hour tutorial class.