Probability Theory and Mathematical Statistics 2
Introduction to statistical theory; principles of sufficiency and likelihood; point and interval estimation; maximum likelihood; Bayesian inference; hypothesis testing; Neyman-Pearson lemma; likelihood ratio tests; asymptotic results, including delta method; exponential family.
STAT
642
 Hours 3.0 Credit, 3.0 Lecture, 0.0 Lab Prerequisites STAT 641 Taught Winter
Course Outcomes:

#### STAT 642

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

Find sufficient, minimal sufficient, ancillary, and complete statistics

#### Use Methods

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

#### Evaluate Estimators

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

#### Apply Theorems

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

#### Derive Likelihood

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

#### Find UMP Tests

Use the Neyman-Pearson Lemma to find UMP tests

#### Evaluate Tests

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

#### Find Interval Estimators

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

#### Evaluate Interval Estimators

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

#### Evaluate Asymptotic Properties

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

#### Describe Properties

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

#### Use Delta Method

Use delta method to find asymptotic properties of transformed random variables