Statistical Inference

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.