On completing this course, the student will have facility with the concepts of statistical theory fundamental to future work in probability and statistics. The student will be able to:

Find sufficient, minimal sufficient, ancillary, and complete statistics

Use method of moments, maximum likelihood, and the Bayesian approach to find estimators

Evaluate estimators using mean squared error, bias, variance, loss functions, and Monte Carlo methods

Apply the Rao-Blackwell Theorem and Lehmann-Scheffe's Theorem to improve existing estimators

Derive likelihood ratio tests, Bayesian tests, Wald tests, and score tests

Use the Neyman-Pearson Lemma to find UMP tests

Evaluate tests with respect to error probabilities and power using analytical, bookstrap, and other Monte Carlo methods

Find interval estimators by inverting test statistics, using pivotal quantities, and using the Bayesian approach

Evaluate interval estimators with respect to size and coverage probabilities using analytical, bookstrap, and other Monte Carlo methods

Evaluate asymptotic properties of estimators with respect to consistency, asymptotic normality, and asymptotic efficiency

Describe asymptotic properties of estimators with respect to consistency, asymptotic normality, and asymptotic efficiency

Use delta method to find asymptotic properties of transformed random variables