This course introduces students to the basic theory behind the development and assessment of statistical analysis techniques in the areas of point and interval estimation, as well as hypothesis testing. Topics include:
* Point estimation methods, including method of moments and maximum likelihood, bias and variance, mean-squared error, sufficiency, completeness, exponential families, the Cramer-Rao inequality, the Rao-Blackwell theorem, uniformly minimum variance unbiased estimators, and Bayesian estimation methods.
* Confidence interval construction methods, including likelihood-based intervals, inversion methods, intervals based on pivots, Bayesian credible and highest posterior density regions, and resampling based intervals.
* Hypothesis testing methods, including likelihood ratio tests, the Neymann-Pearson lemma and uniformly most powerful tests, power calculations, Bayesian approaches, and non-parametric approaches.
Learning Outcomes
Upon successful completion, students will have the knowledge and skills to:
- Explain in detail the notion of a parametric model and point estimation of the parameters of those models.
- Explain in detail and demonstrate approaches to include a measure of accuracy for estimation procedures and our confidence in them by examining the area of interval estimation.
- Demonstrate the plausibility of pre-specified ideas about the parameters of the model by examining the area of hypothesis testing.
- Explain in detail and demonstrate the use of non-parametric statistical methods.
- Demonstrate in detail computational skills to implement various statistical inferential approaches.
