The goal of this course is to present a review for the most fundamental results in statistical testing. This entails reviewing the Neyman-Pearson Lemma for simple hypotheses and the Karlin-Rubin Theorem for monotone likelihood ratio parametric families. The students will also encounter the important concept of p-values and their use in some multiple testing situations. Further methods for constructing tests will be also presented including likelihood ratio and chi-square tests. Some non-parametric tests will be reviewed such as the Kolmogorov goodness-of-fit test and the two sample Wilcoxon rank test. The most important theoretical results will be reproved and also illustrated via different examples. Three sessions of exercises will be scheduled (the students will be handed in an exercise sheet a week before discussing solutions in class).
All the course material can be found on Moodle.
February 22, 2021:
Beginning of lecture: Thursday, 25.02.2021.
- Statistical Inference (Casella and Berger)
- Testing Statistical Hypotheses (Lehmann and Romano)