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.
- Statistical Inference (Casella and Berger)
- Testing Statistical Hypotheses (Lehmann and Romano)